She's trying to communicate something with the nipping. With my rabbits it means they usually want me to put them down, but since your bun is running back to you when you do put her down, my guess would be that's not what she's trying to tell you. Hormones are a possible cause, and if so spaying can help. But if it's not hormones it could be she wants you to give her head rubs, she wants treats, she wants you to play rabbit games with her, she wants you to move out of her way or somewhere else. Sometimes they want down because they need to pee, but it doesn't sound like it's this with your bun. When my rabbits are trying to tell me something I'll just start going through the list of possibilities until I hit on the thing they are trying to tell me.
But even though you are trying to figure out what she is trying to communicate with you, you still don't want to encourage the nipping. So I would give a loud 'yelp', then if she continues 'yelp' again and put her down, then try and figure out what she was trying to communicate with you. Unless she wants you to put her down, then I would shoo her back into her cage for a timeout.
Reading up on rabbit communication might be helpful too.
http://language.rabbitspeak.com/
For spaying, just find the best rabbit vet you can. Though there is always risk with any surgery, having an experienced rabbit vet do it can reduce those risks. If they do pre surgery blood work, intubate, do an IV line, these can all help reduce the risks as well, though it does also add to the cost.
https://rabbit.org/vet-listings/
http://www.bio.miami.edu/hare/opcare.html
