This is a tough one. I would perhaps insist that she spend one day 'shadowing' the gifted program before she decides if it's for her.
I would also suggest that she take notes on her questions and then ask them later during office hours or via email. Or bring them to the family dinner table, or do 'google races' with you or you and some siblings later.
It is a bit of an adjustment to teachers who teach 100 students a day. It would be fun to make a game out if it. Perhaps give DD 10 buttons and ask her to give you 'the blue one' or 'the biggest one' or 'the nicest 3' through out the day. Then the next day give her 100 buttons, and ask the same sorts of questions. I'll bet she could do it, but would gain a hands on experience of how much harder it is.
The advantage of middle school is that one doesn't have to spend all day with a teacher that 'doesn't like' one.
Best Wishes,
Grinity