Debt Instrument, Cap Interest Rate

No definition available.

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Period Type:	duration

- Definition

Debt Instrument, Floor Interest Rate

+ References

No definition available.

+ Details

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Balance Type:	na
Period Type:	duration

- Definition

Debt Instrument, Redemption Price, Annual Increase In Percentage

+ References

No definition available.

+ Details

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Balance Type:	na
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- Definition

Line of Credit Facility, Available Increase In Borrowing Capacity

+ References

No definition available.

+ Details

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

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

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Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, before unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but is not limited to, notes payable, bonds payable, commercial loans, mortgage loans, convertible debt, subordinated debt and other types of debt.

+ References

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+ Details

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

- Definition

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

+ References

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+ Details

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

- Definition

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

+ References

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-SubTopic 10
-Name Accounting Standards Codification
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+ Details

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

- Definition

Amount of principal of debt issued.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 10
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-Section S99
-Paragraph 3
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+ Details

Name:	us-gaap_DebtInstrumentIssuedPrincipal
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Percentage price of original principal amount of debt at which debt can be redeemed by the issuer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 470
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-Section 50
-Paragraph 3
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+ Details

Name:	us-gaap_DebtInstrumentRedemptionPricePercentage
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Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Fair value amount of debt instrument that was repurchased.

+ References

No definition available.

+ Details

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

- Definition

Amount, after accumulated amortization, of debt discount.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 835
-SubTopic 30
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+ Details

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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
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Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Gross amount of debt extinguished.

+ References

No definition available.

+ Details

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

- Definition

Difference between the fair value of payments made and the carrying amount of debt which is extinguished prior to maturity.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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

- Definition

The carrying value as of the balance sheet date of the current and noncurrent portions of long-term obligations drawn from a line of credit, which is a bank's commitment to make loans up to a specific amount. Examples of items that might be included in the application of this element may consist of letters of credit, standby letters of credit, and revolving credit arrangements, under which borrowings can be made up to a maximum amount as of any point in time conditional on satisfaction of specified terms before, as of and after the date of drawdowns on the line. Includes short-term obligations that would normally be classified as current liabilities but for which (a) postbalance sheet date issuance of a long term obligation to refinance the short term obligation on a long term basis, or (b) the enterprise has entered into a financing agreement that clearly permits the enterprise to refinance the short-term obligation on a long term basis and the following conditions are met (1) the agreement does not expire within 1 year and is not cancelable by the lender except for violation of an objectively determinable provision, (2) no violation exists at the BS date, and (3) the lender has entered into the financing agreement is expected to be financially capable of honoring the agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
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+ Details

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

- References

No definition available.

+ Details

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Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- 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

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
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+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
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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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 10
-Name Accounting Standards Codification
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+ Details

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

- Details

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Data Type:	na
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Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_A712SeniorNotesMaturingMarch2031Member
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- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_A634SeniorNotesMaturingMarchof2025Member
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Period Type:

- Details

Name:	bzh_LongtermandShorttermDebtTypeAxis=us-gaap_JuniorSubordinatedDebtMember
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Balance Type:
Period Type:

- Details

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- Details

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- Details

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Period Type:

- Details

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Borrowings - Narrative (Details) - USD ($)			1 Months Ended		3 Months Ended			6 Months Ended
Borrowings - Narrative (Details) - USD ($)	Jun. 01, 2022	Jun. 01, 2012	Mar. 31, 2024	Jan. 31, 2010	Mar. 31, 2025	Mar. 31, 2024	Dec. 31, 2023	Mar. 31, 2025	Mar. 31, 2024	Jan. 28, 2025	Jan. 27, 2025	Sep. 30, 2024
Line of Credit Facility [Abstract]
Debt repurchased					$ 0			$ 0
Loss on extinguishment of debt, net					$ 0	$ 424,000		$ 0	$ 437,000
Senior Notes \| 7.500%
Line of Credit Facility [Abstract]
Debt instrument, issued, principal						$ 250,000,000
Stated interest rate on debt instrument					7.50%			7.50%				7.50%
Senior Notes \| 6 .750% Senior Notes Maturing March of 2025
Line of Credit Facility [Abstract]
Extinguishment of debt			$ 197,900,000				$ 4,300,000
Stated interest rate on debt instrument							6.75%
Loss on extinguishment of debt, net			$ 400,000				$ 100,000
Junior Subordinated Notes
Line of Credit Facility [Abstract]
Unamortized accretion					$ 23,336,000			$ 23,336,000				$ 24,369,000
Junior Subordinated Notes
Line of Credit Facility [Abstract]
Aggregate principle balance of notes					$ 100,800,000			$ 100,800,000
Weighted average fixed interest rate of debt					7.00%			7.00%
Junior Subordinated Debt, Modified Terms
Line of Credit Facility [Abstract]
Aggregate principal amount of debt				$ 75,000,000.0
Variable rate floor				4.25%
Variable rate cap				9.25%
Redemption price percentage		75.00%
Annual increase of percentage of principal amount redeemable	1.785%
Junior Subordinated Debt, Original Terms
Line of Credit Facility [Abstract]
Aggregate principal amount of debt					$ 25,800,000			$ 25,800,000
Basis spread on variable rate				2.71%
Senior Unsecured Revolving Credit Facility
Line of Credit Facility [Abstract]
Credit facility, maximum borrowing capacity, including letters of credit					400,000,000			400,000,000
Credit facility, available increase in borrowing capacity					35,000,000			35,000,000
Senior unsecured revolving credit facility					55,000,000			55,000,000				0
Letters of credit secured using cash collateral					17,400,000			17,400,000
Amount of available borrowings under the secured revolving credit facility					292,600,000			292,600,000
Senior Unsecured Revolving Credit Facility \| Senior Notes
Line of Credit Facility [Abstract]
Credit facility, maximum borrowing capacity, including letters of credit					365,000,000			365,000,000		$ 365,000,000	$ 300,000,000
Letter of Credit
Line of Credit Facility [Abstract]
Letters of credit secured using cash collateral					21,900,000			21,900,000				$ 36,400,000
Letter of Credit \| Senior Notes
Line of Credit Facility [Abstract]
Credit facility, maximum borrowing capacity, including letters of credit					$ 100,000,000.0			$ 100,000,000.0