Debt Instrument, Covenant, Aggregate Amount Of Other Investments Permitted

No definition available.

Name:	bzh_DebtInstrumentCovenantAggregateAmountOfOtherInvestmentsPermitted
Namespace Prefix:	bzh_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Debt Instrument, Face Amount, Modification

+ References

No definition available.

+ Details

Name:	bzh_DebtInstrumentFaceAmountModification
Namespace Prefix:	bzh_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Debt Instrument, Interest Rate, Effective Period

+ References

No definition available.

+ Details

Name:	bzh_DebtInstrumentInterestRateEffectivePeriod
Namespace Prefix:	bzh_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Instrument, Minimum Housing Collateral Ratio

+ References

No definition available.

+ Details

Name:	bzh_DebtInstrumentMinimumHousingCollateralRatio
Namespace Prefix:	bzh_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Definition

Debt Instrument, Minimum Liquidity, Amount

+ References

No definition available.

+ Details

Name:	bzh_DebtInstrumentMinimumLiquidityAmount
Namespace Prefix:	bzh_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Debt Instrument, Minimum Liquidity Covenant, Interest Coverage Ratio

+ References

No definition available.

+ Details

Name:	bzh_DebtInstrumentMinimumLiquidityCovenantInterestCoverageRatio
Namespace Prefix:	bzh_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Definition

Debt Instrument, Minimum Liquidity, Outside of Initial Requirements, Amount

+ References

No definition available.

+ Details

Name:	bzh_DebtInstrumentMinimumLiquidityOutsideOfInitialRequirementsAmount
Namespace Prefix:	bzh_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line of Credit Facility, Number of Lenders

+ References

No definition available.

+ Details

Name:	bzh_LineofCreditFacilityNumberofLenders
Namespace Prefix:	bzh_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Ownership Interest In Guarantor Subsidiaries

+ References

No definition available.

+ Details

Name:	bzh_OwnershipInterestInGuarantorSubsidiaries
Namespace Prefix:	bzh_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=119993939&loc=d3e28551-108399

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=114775985&loc=d3e28878-108400

+ Details

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

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of the required periodic payments including both interest and principal payments.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22)
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=75038535&loc=d3e64711-112823

+ Details

Name:	us-gaap_DebtInstrumentPeriodicPayment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount, after accumulated amortization, of debt discount.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 1A
-URI http://asc.fasb.org/extlink&oid=119993939&loc=d3e28541-108399

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=114775985&loc=d3e28878-108400

+ Details

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

- Definition

Weighted average interest rate of debt outstanding.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

The total amount of the contingent obligation under letters of credit outstanding as of the reporting date.

+ References

No definition available.

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount of current borrowing capacity under the credit facility considering any current restrictions on the amount that could be borrowed (for example, borrowings may be limited by the amount of current assets), but without considering any amounts currently outstanding under the facility.

+ References

+ Details

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

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

+ Details

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

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

+ References

+ Details

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

- References

No definition available.

+ Details

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

- References

No definition available.

+ Details

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

- Details

Name:	bzh_LongtermandShorttermDebtTypeAxis=us-gaap_JuniorSubordinatedDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=bzh_LetterofCreditCashSecuredMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_StandbyLettersOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_StandbyLetterforCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_BackstopStandbyLettersofCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_JuniorSubordinatedDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_SeniorUnsecuredTermLoanSeptember2022Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Borrowings - Narrative (Details)	Sep. 09, 2019 USD ($)	Jul. 30, 2016	Dec. 31, 2020 USD ($) lender	Oct. 08, 2020 USD ($)	Sep. 30, 2020 USD ($)	May 31, 2018 USD ($)	Jan. 31, 2010 USD ($)
Line of Credit Facility [Abstract]
Amount of available borrowings under the secured revolving credit facility			$ 250,000,000.0
Senior Notes [Abstract]
Ownership interest In guarantor subsidiaries			100.00%
Junior Subordinated Notes
Unsecured Debt [Abstract]
Stated interest rate on debt instrument		7.987%
Junior Subordinated Notes [Abstract]
Effective period of debt instrument interest rate		10 years
Face amount modification							$ 75,000,000.0
Unamortized accretion			$ 32,120,000		$ 32,636,000
Revolving Credit Facility
Line of Credit Facility [Abstract]
Credit facility borrowing capacity			$ 250,000,000.0
Number of lenders \| lender			4
Covenant, aggregate amount of other investments				$ 300,000,000.0
Minimum liquidity covenant, interest coverage ratio				1.00
Minimum housing collateral ratio				1.75
Minimum liquidity, amount				$ 50,000,000.0
Minimum liquidity, outside of initial requirements, amount				$ 100,000,000.0
Borrowings outstanding			$ 0		0
Letters of credit secured using cash collateral			0		0
Letter of Credit, Cash Secured
Line of Credit Facility [Abstract]
Letters of credit secured using cash collateral			11,700,000		$ 12,700,000
Standby Letters of Credit \| Standby Letters for Credit Facility
Line of Credit Facility [Abstract]
Credit facility borrowing capacity						$ 50,000,000.0
Letters of credit secured using cash collateral			$ 25,700,000
Standby Letters of Credit \| Backstop Standby Letters of Credit
Line of Credit Facility [Abstract]
Credit facility borrowing capacity						$ 40,000,000.0
Junior Subordinated Notes
Junior Subordinated Notes [Abstract]
Weighted average fixed interest rate of debt			4.25%
Senior Notes \| Senior Unsecured Term Loans September 2022
Unsecured Debt [Abstract]
Aggregate principal amount of debt	$ 100,000,000.0
Periodic payment	$ 50,000,000.0
Stated interest rate on debt instrument	4.875%