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Stock-Based Compensation Plans (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Dec. 31, 2011
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of Shares Authorized 19,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized      
Number of Shares Available for Grant 1,800,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant      
Share-based Compensation Arrangement by Share-based Payment Award, Expiration Period 10 years 0 months 0 days      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]        
Granted $ 1.14us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 1.84us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 1.32us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue  
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Compensation expense for the year $ 3.3us-gaap_ShareBasedCompensation $ 4.9us-gaap_ShareBasedCompensation $ 5.2us-gaap_ShareBasedCompensation  
Cash received from awards exercised 1.3us-gaap_ProceedsFromStockOptionsExercised 7.1us-gaap_ProceedsFromStockOptionsExercised 12.1us-gaap_ProceedsFromStockOptionsExercised  
Intrinsic Value of awards exercisable 0.4us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1      
Intrinsic Value of awards outstanding 0.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term 5 years      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term 3 years      
Phantom Shares Annual Grant 0cbb_PhantomSharesAnnualGrant     6,000cbb_PhantomSharesAnnualGrant
Deferred Compensation Plans, Years of Service Required for Full Vesting five      
Stock Options and Stock Appreciation Rights [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period 3 years 0 months 0 days      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]        
Outstanding at January 1, 6,128,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
9,538,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
14,152,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Outstanding at January 1, $ 3.66us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 4.04us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 3.70us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Granted 998,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
595,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
994,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Granted $ 3.41us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 4.75us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 3.41us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Exercised (725,000)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(804,000)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(4,854,000)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Exercised $ 1.73us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 2.41us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 2.80us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Forfeited 215,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(361,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(6,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Forfeited $ 3.99us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 3.39us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 2.91us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Expired (962,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(2,840,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(748,000)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Expired $ 3.73us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 5.56us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 4.87us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Outstanding at December 31, 5,224,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
6,128,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
9,538,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Outstanding at December 31, $ 3.85us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 3.66us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 4.04us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Expected to vest at December 31, 5,224,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
6,128,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
9,538,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Expected to vest at December 31, $ 3.85us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 3.66us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 4.04us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Exercisable at December 31, 3,477,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
5,064,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
8,486,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Exercisable at December 31, $ 3.98us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 3.61us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
$ 4.13us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Compensation expense for the year 0.3us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
0.6us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
1.1us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Tax benefit related to compensation expense (0.1)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(0.2)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
(0.4)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Intrinsic value of awards exercised 1.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
1.2us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
10.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Cash received from awards exercised 1.3us-gaap_ProceedsFromStockOptionsExercised
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
2.4us-gaap_ProceedsFromStockOptionsExercised
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
5.5us-gaap_ProceedsFromStockOptionsExercised
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Grant date fair value of awards vested 0.4cbb_SharebasedCompensationArrangementbyShareBasedPaymentAwardStockOptionsandStockAppreciationRightsVestedinPeriodFairValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
0.4cbb_SharebasedCompensationArrangementbyShareBasedPaymentAwardStockOptionsandStockAppreciationRightsVestedinPeriodFairValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
0.5cbb_SharebasedCompensationArrangementbyShareBasedPaymentAwardStockOptionsandStockAppreciationRightsVestedinPeriodFairValue
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
 
Unrecognized Compensation 1.4us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= cbb_StockOptionsAndStockAppreciationRightsMember
     
Employee Service Share-based Compensation, Nonvested Awards, Compensation Cost Not yet Recognized, Period for Recognition 2 years      
Performance Based Awards [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period 3 years      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Compensation expense for the year 1.4us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
2.6us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
2.7us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
 
Tax benefit related to compensation expense (0.5)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
(1.0)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
(1.0)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
 
Unrecognized Compensation 3.6us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
     
Employee Service Share-based Compensation, Nonvested Awards, Compensation Cost Not yet Recognized, Period for Recognition 2 years      
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Grants in Period 1,085,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
1,067,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
808,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedAwardsMember
 
Restricted Stock [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period 3 years      
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Compensation expense for the year 1.6us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
1.7us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
1.5us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Tax benefit related to compensation expense (0.6)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
(0.6)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
(0.6)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Unrecognized Compensation 0.6us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
     
Employee Service Share-based Compensation, Nonvested Awards, Compensation Cost Not yet Recognized, Period for Recognition 1 year      
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Grants in Period 176,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
279,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
725,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Stock Appreciation Rights (SARs) [Member]        
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]        
Granted     $ 1.32us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Grants in Period     531,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Fair Value of Grants in Period     0.8cbb_ShareBasedCompensationArrangementByShareBasedPaymentAwardOtherThanOptionsAggregateFairValueOfGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Aggregate intrinsic value, cash settled and other awards, outstanding 0.3us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
     
Aggregate intrinsic value, cash settled and other awards, exercisable 0.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
     
Performance Based Cash Unit Award [Member]        
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Compensation expense for the year 0.6us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedCashUnitAwardMember
(0.2)us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedCashUnitAwardMember
4.4us-gaap_ShareBasedCompensation
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedCashUnitAwardMember
 
Fair Value of Grants in Period 3.6cbb_ShareBasedCompensationArrangementByShareBasedPaymentAwardOtherThanOptionsAggregateFairValueOfGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedCashUnitAwardMember
  2.3cbb_ShareBasedCompensationArrangementByShareBasedPaymentAwardOtherThanOptionsAggregateFairValueOfGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cbb_PerformanceBasedCashUnitAwardMember
 
Deferred Compensation, Share-based Payments [Member]        
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]        
Deferred Compensation,Total Shares Deferred 400,000us-gaap_DeferredCompensationArrangementWithIndividualSharesIssued
/ us-gaap_AwardTypeAxis
= us-gaap_DeferredCompensationShareBasedPaymentsMember
700,000us-gaap_DeferredCompensationArrangementWithIndividualSharesIssued
/ us-gaap_AwardTypeAxis
= us-gaap_DeferredCompensationShareBasedPaymentsMember
   
Deferred Compensation, Compensation Expense $ 0.3us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_DeferredCompensationShareBasedPaymentsMember
$ (1.4)us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_DeferredCompensationShareBasedPaymentsMember
$ 1.8us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_DeferredCompensationShareBasedPaymentsMember