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Summary of Significant Accounting Policies (Details 5) (USD $)
12 Months Ended
Dec. 31, 2014
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Dec. 31, 2013
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Jul. 31, 2013
Dec. 31, 2012
Restrictions on Cash        
Amount of cash reserves with Federal Reserve Bank $ 2,300,000us-gaap_RestrictedCashAndCashEquivalents      
Operating Segments        
Number of active operating subsidiaries 1byfc_NumberOfActiveOperatingSubsidiaries 1byfc_NumberOfActiveOperatingSubsidiaries    
Number of reportable business segments 1us-gaap_NumberOfReportableSegments      
Adoption of New Accounting Standards        
Unrecognized tax benefits $ 475,000us-gaap_UnrecognizedTaxBenefits $ 488,000us-gaap_UnrecognizedTaxBenefits $ 0us-gaap_UnrecognizedTaxBenefits $ 431,000us-gaap_UnrecognizedTaxBenefits