For what it's worth, I also think the name looks like Betteris, although I can see how it could be mistranscribed. But there aren't two vowels in the middle, so even if the e was misread as an o, it still wouldn't spell Wootons. It could spell Wotteris, or maybe Wottens, if you ignore the dot over the i, but like you, I think the initial letter is a B, and the last three letters are ris.
I always wonder why names and words vary so much in spelling (I know there was no standard at this time), and in this case I'd suspect it's been 'misspelt' (to our way of thinking) because her name wasn't pronounced the way we pronounce it today. This could be because of local dialect, or even the idiosyncracies of her own family's way of referring to each other, with 'pet' names, and so on. And they may never have seen the name written down. So instead of Bee-a-triss, as we would say today (and even that's subject to dialect, because some people pronounce it Bay-a-triss, depending on where they come from) maybe it was pronounced Bett-riss. An extra e in the middle wouldn't necessarily change the pronunciation - Bette-riss. Rather than the Better-iss that we could read it as.
Just my thoughts, and ramblings, and might be completely wrong, but this sort of stuff fascinates me!
