Share-based Compensation - Unvested Restricted Shares (Details) - Stock Incentive Plan [Member] - Restricted Shares [Member] - $ / shares	6 Months Ended
Jun. 30, 2019	Jun. 30, 2018
Unvested Restricted Shares [Roll Forward]
Unvested at beginning of period (in shares)	22,569	18,062
Granted (in shares)	12,058	11,527
Vested (in shares)	(10,033)	(6,652)
Forfeited or surrendered (in shares)	(960)	(368)
Unvested at end of period (in shares)	23,634	22,569
Unvested Restricted Shares, Weighted Average Grant Date Fair Value Per Share [Roll Forward]
Unvested at beginning of period (in dollars per share)	$ 17.98	$ 16.44
Granted (in dollars per share)	21.69	21.47
Vested (in dollars per share)	21.63	21.47
Forfeited or surrendered (in dollars per share)	21.27	21.47
Unvested at end of period (in dollars per share)	$ 20.10	$ 17.98

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(3)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(3)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(1)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(1)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)-(ii)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

The weighted average fair value of nonvested awards on equity-based plans excluding option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, revenue or profit achievement stock award plan) for which the employer is contingently obligated to issue equity instruments or transfer assets to an employee who has not yet satisfied service or performance criteria necessary to gain title to proceeds from the sale of the award or underlying shares or units.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)-(ii)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(2)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(2)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_PlanNameAxis=fbss_StockIncentivePlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: