I like both a lot,
Beatrix being my favorite at the moment. I think Bibi's a pretty cute nickname or just B. I don't care much for
Trix or
Trixie.
I like
Beatrice pronounced the Italian way, as Beh-uh-tri-che. But pronounced the usual way's fine too, as it's a character I liked in Shakespeare.
A tip for middle names . . . try finding a name in the same language that you like. Usually, a name in the same language, say Late
Roman, will flow well. But rules are always there to be broken. A few combos:
Beatrix AmandusBeatrix ClaritiaBeatrix DominicaBeatrix Fidelis
That's all I can think of? Sorry, too hot to think right now.