hi there,
have just had a look at this: the Wiltshire bmd is showing a structure of children for William... being an un-named, Mary and Elizabeth at Potterne to spouse Tyler......
family search.org is showing structures for William/Mary-Anne(nee tyler) at Potterne, a Richard/Martha at Uchfont and a Maria as soul parent on records also at Potterne......
realistically unless you can find the child on the freebmduk as Banks (which for Wiltshire may be hard to distinguish from other Banks branches in the county) I would say its going to be almost impossible to find "ye bastard child" unless Maria is the mother......
sorry I cannot be of more assistance with this request
fusion