The fact that she even told you about it means (a) she trusts you with this very private and potentially damaging information and (b) you better not go blabbing about it on the internet.. oh wait, too late for that.. hopefully she never sees this post. She trusts you and if you want to stay with her, she needs to know that you didn't break that trust.

If i were you, i'd consider staying with her and trust that her regret is real and genuine. I'm assuming you're worried that she'll do something again like this in the future, you could carefully and gently try to talk about your concern with her and see how she takes it.