1) Do you think it's unforgivably arrogant to change your own name to
Bella?
Definitely not.
Bella does mean beautiful, but I don't think it's arrogant because it's a common name and the meaning isn't really really obvious. Not like actually calling yourself "beautiful" in English!
2) If I like
Isabella nn
Bella, what other names might make the cut?
Isabella is so common, so you could choose a more interesting name which can also use the nickname
Bella, such as
Arabella or
Annabel