Loans and Allowance for Loan Losses - Additional Information (Details) $ in Millions	3 Months Ended	6 Months Ended
Jun. 30, 2019 USD ($) Loan Property	Jun. 30, 2018 Loan Property	Jun. 30, 2019 USD ($) Loan Property	Jun. 30, 2018 Loan Property	Dec. 31, 2018 USD ($) Loan
Troubled Debt Restructurings [Abstract]
Number of Contracts	0	0	0	0
Number of TDR loans in the portfolio	4		4		6
TDR loans in the portfolio \| $	$ 2.9		$ 2.9		$ 3.4
Number of TDR loans current and performing	4		4		5
Number of TDRs with defaults occurring within 12 months of modification	0	0	0	0
Residential Real Estate [Member]
Troubled Debt Restructurings [Abstract]
Number of foreclosed properties in possession or in process of foreclosure \| Property	0	0	0	0

Number of foreclosed properties in possession or in the process of foreclosure.

No definition available.

Name:	fbss_NumberOfForeclosedPropertiesInPossessionOrInProcessOfForeclosure
Namespace Prefix:	fbss_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

The number of troubled debt restructuring loans outstanding in the portfolio.

+ References

No definition available.

+ Details

Name:	fbss_NumberOfTDRLoansOutstanding
Namespace Prefix:	fbss_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Represents the number of troubled debt restructuring loans that are current and performing in accordance with modified terms.

+ References

No definition available.

+ Details

Name:	fbss_NumberOfTdrLoansCurrentAndPerforming
Namespace Prefix:	fbss_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of financing receivables that have been modified by troubled debt restructurings.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 33
-URI http://asc.fasb.org/extlink&oid=84173941&loc=SL6953676-111524

+ Details

Name:	us-gaap_FinancingReceivableModificationsNumberOfContracts2
Namespace Prefix:	us-gaap_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

The amount of the outstanding recorded investment related to financing receivables that have been modified by troubled debt restructurings.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 40
-Section 50
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=82895541&loc=d3e18845-111554

+ Details

Name:	us-gaap_FinancingReceivableModificationsRecordedInvestment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Number of financing receivables that have been modified by troubled debt restructurings within the previous 12 months and for which there was a payment default.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 34
-URI http://asc.fasb.org/extlink&oid=84173941&loc=SL6953682-111524

+ Details

Name:	us-gaap_FinancingReceivableModificationsSubsequentDefaultNumberOfContracts1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_ReceivablesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=us-gaap_ResidentialPortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: