It sounds like you're doing the right stuff for her.
I'm kind of surprised she has a diagnosis of Bipolar at the age of 7. Is she adopted? Or did she have a period of neglect in early childhood due to illness in the family, etc? The reason I ask is this sounds a lot like an attachment disorder.
Best wishes -
it is possible that this is part of her being bi polar, may I ask if she takes any meds,it may be as you say that being an only child does play some part in her neediness for others to play with .What about Drawing, painting ,more absorbing games, how about playing board games with her ,getting her mind involved, jigsaw puzzles can be fun and keep them busy ,Does she get plenty of physical exercise as many children do well when they are active regularly ..