By the look of the Index to the 1841 census there were more children than just two.
Ann Bays born Jarrow c1830, Joseph Bays c1835, Catherine Bays c1836, John Bays c1838, William Bays c1841.
IGI has Catherine's baptism in St Hilda as BAIS (1833), a Joseph BAYS in 1835, and a Robert Russell BAES in 1827.
A copy of the birth cert of John or William should give you Catherine's maiden name to further assist you find the marriage which may have been mistranscribed (eg 'Boys, Bais, Baes, Bayes'). Perhaps James parents appear on that marriage entry or a sibling is down as a witness.
St Hilda, County Durham would seem to be a good place to start looking for the marriage. Roy G