Does your daughter have a hobby she enjoys? My son is not much older than yours, and he has repeatedly told me he doesn't fit in with the kids at school, and he has wanted to homeschool since kindergarten. Now, his situation is slightly different because thus far there has been no bullying. He gets along ok with the kids at school, but he really has no interest in socializing with them outside of school, and he's fine being the kid on the periphery at school.
However, he has found 2-3 kids with whom he has gotten quite close, and he found them through outside interests (an individual sport). At least locally, the kids who play individual sports like tennis, golf, swimming, and martial arts seem to be much more like my son. Perhaps not all of them are "gifted", but then I don't technically know that my son is either. But they *tend* to be readers, play chess, like legos and board games, etc., and thus my son has found a few kindred souls.
If you haven't introduced her to an individual sport, you might try one. Tennis has the Quickstart program these days which makes it much more accessible to younger kids, most medium sized towns seem to have swimming leagues nowadays, though of course your options depend on location.
If she truly seems to be ok with the situation, you might believe her (and maintain a watchful eye). Some people prefer quality of friends over large social circles, and your daughter may be one. Good luck and I hope the bullying can be remedied.
On edit- After reading some of your additional posts, I agree with at least keeping the spectrum issues in mind. We've never had him tested, but I do think my son is very, very, very mildly an Aspie or on the spectrum. He likes things to be ordered and tidy, he has little patience for those who don't understand things as quickly/easily as he does, and he wants things done a certain way. While I think that has played some role in his friendship issues, I really think for him it has been more of a combination of finding kids with similar interests and his introversion. You just never know with these kids!
