Well, I don't really like it, for a couple of reason. One is that I think the pronunciation thing would do me in - I have always heard of
Bette as "bet" (like Midler, as you say), and I would expect bet-ee to be spelt
Betty. So I personally would never guess the right pronunciation. But also...it feels really unfinished to me. There are some single syllable names that I really enjoy (
May,
Leigh,
Kay) but I kind of feel like there's something missing from
Bette.
Ah, maybe it's just me.
As far as using it as a nickname for
Elizabeth - I guess that's a pretty good scenario, as far as my view is concerned, anyway, because she can always fall back on her full name later in life. And there are certainly a lot of worse names than
Bette - it's just not really my cup of tea. Anyway, if I were using
Elizabeth, she would be
Beth all the way, so no other nickname would get a look in (though I think I'm in the majority with that - I think most people on here don't like
Beth much! More for me, I say :-D )