Wow! really!! I clip kitties nails all the time (not my own kitties I am talking about) and have not gotten bitten yet. Perhaps she was feed up of being handled.
Try to get her use to have her paws touched. Just rub them a few seconds every day - all 4 of them, touch her nails too with your fingers. It could take many months to have her use to it but don't stop.
I did that with my kitties and it takes me 30 seconds to clip all 4 paws.