A lot of the time, the biting is due to over-stimulization. The kitten starts playing and gets more and more excited and doesn't know how to handle all that adrenaline and emotion.
Try giving the kitten a "time out". When she gets excited like that, take her and place her in a nice quiet darkened room, then walk out. She'll be able to come down from her adrenaline high. As she gets older, she'll be better able to handle things.
The other suggestion is to watch what sets her off. Many cats have a "sensitive" spot on their bodies - they don't like being touched there and will bite when you do. For most cats, it is their tail, the base of the tail, and/or their stomach. Some cats are sensitive on the top of their head/ears. When you pet, softly and slowly just slide your hand along the base of the head to mid back. No more than that. Don't pat, rub against the fur, etc. The soft, slow motion will best help relax her. If she starts getting excited even with that, try the "time out". Some cats never want more than this minimal petting - anything more and they lash out.