Bet doesn't really have enough solos or a large enough range to warrant belting, I think. Our Bet last year was hardly a good singer but she hit all the notes in her chest voice--she had a deeper, more alto-y voice, though she could sing soprano when she needed to.
Don't scream or strain yourself, but be sure to accent the lyrics and put emphasis on the right words (No flounces, no FEATHERS, no frills or furbiloes). At least, that's how it sounds on the OBC. Just sing with a loud voice; really, Bet isn't that difficult of a role (vocally). Have fun and let us know how it's going!