Leases - Maturity Schedule of Undiscounted Cash Flows Contribute to Lease Liability (Details) $ in Thousands	Sep. 30, 2019 USD ($)
Leases [Abstract]
Three months ending December 31, 2019	$ 111
Twelve months ending December 31, 2020	670
Twelve months ending December 31, 2021	682
Twelve months ending December 31, 2022	694
Twelve months ending December 31, 2023	707
Twelve months ending December 31, 2024	646
Thereafter	2,603
Total undiscounted cash flows	6,113
Less: Discount	(925)
Lease liability	$ 5,188

Lessee operating lease liability payments due after year six.

No definition available.

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Namespace Prefix:	fbss_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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- Definition

Lessee operating lease liability payments due year six.

+ References

No definition available.

+ Details

Name:	fbss_LesseeOperatingLeaseLiabilityPaymentsDueYearSix
Namespace Prefix:	fbss_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

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- Definition

Amount of lessee's undiscounted obligation for lease payments for operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918701-209980

+ Details

Name:	us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments for operating lease, due in fifth fiscal year following latest fiscal year.

+ References

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments for operating lease, due in fourth fiscal year following latest fiscal year.

+ References

+ Details

Name:	us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments for operating lease, due in third fiscal year following latest fiscal year.

+ References

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments for operating lease, due in second fiscal year following latest fiscal year.

+ References

+ Details

Name:	us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments for operating lease having an initial or remaining lease term in excess of one year due in remainder of fiscal year following latest fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918701-209980

+ Details

Name:	us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for operating lease.

+ References

+ Details

Name:	us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=77888419&loc=SL77918627-209977

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant