Loans and Allowance for Loan Losses - Schedule of Past Due Status of Loans (Details) - USD ($) $ in Thousands	Sep. 30, 2019	Dec. 31, 2018
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	$ 4,220	$ 6,823
Current	541,007	542,541
Total Loans	545,227	549,364
90+ days past due and accruing	867	1,227
Nonaccruals	1,941	1,993
30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	1,170	3,591
60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	398	387
90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	2,652	2,845
Commercial and Industrial [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	265	442
Current	27,828	26,279
Total Loans	28,093	26,721
90+ days past due and accruing	0	0
Nonaccruals	246	135
Commercial and Industrial [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	18	365
Commercial and Industrial [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	1	0
Commercial and Industrial [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	246	77
Commercial Real Estate [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	989	1,346
Current	178,436	186,451
Total Loans	179,425	187,797
90+ days past due and accruing	0	0
Nonaccruals	989	974
Commercial Real Estate [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	372
Commercial Real Estate [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	0
Commercial Real Estate [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	989	974
Construction and Land [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	1,419
Current	66,331	69,990
Total Loans	66,331	71,409
90+ days past due and accruing	0	0
Nonaccruals	0	0
Construction and Land [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	1,419
Construction and Land [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	0
Construction and Land [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	0
Consumer [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	2	25
Current	5,557	5,537
Total Loans	5,559	5,562
90+ days past due and accruing	0	0
Nonaccruals	0	0
Consumer [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	2	7
Consumer [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	18
Consumer [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	0
Student [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	1,482	2,212
Current	6,722	6,946
Total Loans	8,204	9,158
90+ days past due and accruing	867	1,227
Nonaccruals	0	0
Student [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	218	747
Student [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	397	238
Student [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	867	1,227
Residential Real Estate [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	894	409
Current	218,792	205,536
Total Loans	219,686	205,945
90+ days past due and accruing	0	0
Nonaccruals	155	317
Residential Real Estate [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	894	278
Residential Real Estate [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	131
Residential Real Estate [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	0
Home Equity Lines of Credit [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	588	970
Current	37,341	41,802
Total Loans	37,929	42,772
90+ days past due and accruing	0	0
Nonaccruals	551	567
Home Equity Lines of Credit [Member] \| 30-59 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	38	403
Home Equity Lines of Credit [Member] \| 60-89 Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	0	0
Home Equity Lines of Credit [Member] \| 90+ Days Past Due [Member]
Financing Receivable, Recorded Investment, Aging [Abstract]
Past due	$ 550	$ 567

Amount of financing receivable 90 days or more past due and still accruing.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 16
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=119407570&loc=SL82919258-210447

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 7
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=118936363&loc=d3e5111-111524

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 55
-Paragraph 80
-URI http://asc.fasb.org/extlink&oid=118955255&loc=SL82922355-210448

+ Details

Name:	us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

Amount of financing receivable not past due.

+ References

+ Details

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

- Definition

Amount of financing receivable on nonaccrual status.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 7
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=118936363&loc=d3e5111-111524

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 16
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=119407570&loc=SL82919258-210447

+ Details

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

- Definition

Amount of financing receivable past due.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 55
-Paragraph 80
-URI http://asc.fasb.org/extlink&oid=118955255&loc=SL82922355-210448

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 14
-URI http://asc.fasb.org/extlink&oid=119407570&loc=SL82919253-210447

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 7A
-URI http://asc.fasb.org/extlink&oid=118936363&loc=SL6953401-111524

+ Details

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

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=118952595&loc=d3e4428-111522

+ Details

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

- Details

Name:	us-gaap_FinancingReceivablesPeriodPastDueAxis=us-gaap_FinancingReceivables30To59DaysPastDueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablesPeriodPastDueAxis=us-gaap_FinancingReceivables60To89DaysPastDueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablesPeriodPastDueAxis=us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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