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Debt (Details) (USD $)
9 Months Ended 0 Months Ended
Dec. 31, 2014
Dec. 31, 2013
May 07, 2014
Mar. 31, 2014
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt $ 1,635,944,000us-gaap_LongTermDebt     $ 1,658,919,000us-gaap_LongTermDebt
Less: Current portion of long-term debt (51,875,000)us-gaap_LongTermDebtCurrent     (73,688,000)us-gaap_LongTermDebtCurrent
Long-term debt, net of current portion 1,584,069,000us-gaap_LongTermDebtNoncurrent     1,585,231,000us-gaap_LongTermDebtNoncurrent
Repayment of debt (219,188,000)us-gaap_RepaymentsOfDebt (289,406,000)us-gaap_RepaymentsOfDebt    
Long-term debt, unamortized discount 14,500,000us-gaap_DebtInstrumentUnamortizedDiscount     12,300,000us-gaap_DebtInstrumentUnamortizedDiscount
Secured Debt | Term Loan A        
Long-term Debt, Current and Noncurrent [Abstract]        
Interest rate 2.66%us-gaap_DebtInstrumentInterestRateEffectivePercentage
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    2.65%us-gaap_DebtInstrumentInterestRateEffectivePercentage
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Long-term debt 806,193,000us-gaap_LongTermDebt
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    660,317,000us-gaap_LongTermDebt
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Term loan, face amount 830,000,000us-gaap_DebtInstrumentFaceAmount
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Quarterly periodic payment percentage, principal     1.25%bah_DebtInstrumentQuarterlyPeriodicPaymentPercentagePrincipal
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Quarterly principal periodic payment percentage, year two     1.875%bah_DebtInstrumentQuarterlyPeriodicPaymentPercentagePrincipalYearTwo
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Quarterly principal periodic payment percentage, year three     2.50%bah_DebtInstrumentQuarterlyPeriodicPaymentPercentagePrincipalYearThree
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Quarterly principal periodic payment percentage, year four     3.125%bah_DebtInstrumentQuarterlyPeriodicPaymentPercentagePrincipalYearFour
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Quarterly principal periodic payment percentage, year five     13.00%bah_DebtInstrumentQuarterlyPeriodicPaymentPercentagePrincipalYearFive
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Secured Debt | Term Loan A | Minimum        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     2.00%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Secured Debt | Term Loan A | Maximum        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     2.75%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Secured Debt | Term Loan A | London Interbank Offered Rate (LIBOR)        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     2.50%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Secured Debt | Term Loan B        
Long-term Debt, Current and Noncurrent [Abstract]        
Interest rate 3.75%us-gaap_DebtInstrumentInterestRateEffectivePercentage
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    3.75%us-gaap_DebtInstrumentInterestRateEffectivePercentage
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Long-term debt 829,751,000us-gaap_LongTermDebt
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    998,602,000us-gaap_LongTermDebt
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Term loan, face amount 841,200,000us-gaap_DebtInstrumentFaceAmount
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Repayment of debt     (168,400,000)us-gaap_RepaymentsOfDebt
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Secured Debt | Term Loan B | Minimum        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     0.75%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Secured Debt | Term Loan B | London Interbank Offered Rate (LIBOR)        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     3.00%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Secured Debt | Term Loan B | London Interbank Offered Rate (LIBOR) | Maximum        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     3.00%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Secured Debt | Term Loan B | Alternative Base Rate (ABR) | Minimum        
Long-term Debt, Current and Noncurrent [Abstract]        
Long-term debt, basis spread on variable rate     2.00%us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
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Revolving Credit Facility        
Long-term Debt, Current and Noncurrent [Abstract]        
Revolving credit facility, maximum borrowing capacity 500,000,000us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
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Revolving credit facility, amount outstanding 0us-gaap_LineOfCredit
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    0us-gaap_LineOfCredit
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Letter of Credit        
Long-term Debt, Current and Noncurrent [Abstract]        
Revolving credit facility, maximum borrowing capacity $ 100,000,000us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
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