Sorry, lanhols, but I disagree with you. There are clear links to Bradford's (including John's) in Woodhouse although nothing in baptisms. I would suggest that Mary and any siblings were baptised in a non-conformist church whose records are not available online.
Indeed, another John Bradford bc.1797 buried 27/1/1828 Non-conformist burial Woodhouse proving a non-conformist link.
Annette