I agree with above posters. I've been bitten many times by my pets (all of them) and I never hit them. I use a firm no and put them back down.
Now granted, I have spanked my children if they misbehaved, but that's a different thing. And it's usually a swat to the bottom and it's usually for something extremely bad, like playing with electrical outlets or the stove. But never EVER will hit them out of anger or reaction because of something like that.
I know you feel bad, I can tell. She is going to take a while again to trust you. Start talking gently to her. Get her to trust YOU then slowly your hand.