Thank you Pat for the extra information.
She is showing classic dominance aggression towards you. Cats who do this, will generally pick one human in the house to display this behavior towards. It is usually the human that does the most for them.
Your the human; she's the cat. She is trying to tell you she is the dominant species. Therefore you play when she wants, feed her when she wants, and leave her alone when she's not in the mood for you any longer.
Here is how you can help stop the behavior, and train her to be the submissive species in house. You can retrain her to teach her that you are dominant figure in the house.
Keep a whistle on you at all times when you are at home. Keep it in your pocket or on a string around your neck. When you see her ready to pounce, blow it. This is going to teach her that behavior of biting you is not acceptable. If she gets by you before you can blow the whistle and bites, properly punish her by putting her in a cat carrier or room by herself for a bit (15 minutes). Separation is a good punishment; smacking or spanking is not.
When she jumps up for attention, put her down immediately. If you have to stand up then stand up and move so she can't have access to your lap. Do this for a couple of weeks. Then when you allow her in your lap, don't let her decide when pet time is over with a nip or bite. You cut her off first. Just pet her for a second put her down and then give her a kitty treat. The treat will teach her to associate the petting with the nice reward. Don't give her kitty treats any other time. This is going to retrain her thought process on who is the dominant one.
You gradually increase the petting time, but always be the one that decides when enough is enough, not her.
There is also a product you can buy at pet smart called feliway. This is a pheromone that inducing calm happy feelings in cats. It is great for aggression, anxiety, urine sprayers, and furniture scratchers. You can get it in a form called comfort zone.
Let me know if you need more help.