Hi Jeff,
I have seen instances of Bahee and Bridget being used for the same person. One was bapt. and married as Bahee, but called "wife Bridget" in the husband's will. Another was married as Bahee, but bapt. and buried as Bridget. This was why I thought your ones might be the same person - especially as the records were in different parishes.
You might have success identifying family connections through wills which you can order on film through LDS Family History Centres. I looked at dozens before locating my correct Radcliife ancestors. Brian Lawson has the indexes and film numbers on his website [messages above this]. It might also be worth checking Bride burials.
The only info. I had about William and Bahee/Bridget was from the IGI, which I put in my previous message. I have more about William and Margery Lace, and the other Radcliffe families - I'll send it to your email directly.
Sue