In terms of cultural reception, there are certainly precedents. Widespread sexist attitudes didn't really slow down Margaret Thatcher, for example; although there was still plenty of that around in the 1950s-1970s, I think she got around it for the simple reason that, while sexism had a lot to say about how women should act at home, it didn't define whether or how women should act as government ministers, simply because the situation had almost never come up before.
Another relevant example would be the Chevalier d'Eon, widely accepted in 18th century society despite being transgendered. If trans people were frequently trying to gain positions at court, they'd have been systematically shut out, but as a one-off it was just seen as an unthreatening curiosity.
So, I could easily believe a one-off instance of a female bishop, especially if she weren't campaigning on the issue of female clergy in general. As long as you can come up with a plausible story as to how she got her foot in the door (demographic exigencies during WWII?), it's not entirely far-fetched that she could distinguish herself and end up a bishop.
There would have been legal obstacles, but I'm sure they could be overcome somehow if everyone played along. The appointment of bishops in England is subject to royal (i.e. government) approval, but that level of the establishment has notoriously always functioned as an old boys' club, not strongly constrained by legal details.