I definitely don't judge you for this - like everyone has said, we've all done stuff we shouldn't have. I'm sure as heck not perfect, so I won't judge someone else for also not being perfect. Honestly, I think it's good that you feel bad about it - because you know that it's wrong. In my opinion, it's up to him to either tell or not. If he does tell, I agree with
Krizstyling, give it like 2 days and call her. I wouldn't give any excuses, like "I was drunk" or something, I would just apologize and let her cuss and scream at you. I also don't really think you'll get an apology, at least not soon, but I'd be more likely to forgive someone if they called and owned up to it, rather than just ignore it and hope it passed.

I would definitely let yourself feel bad, guilty, etc for a *short* while, but don't continually beat yourself up. Hopefully this experience means that you'll never do it again, so grow and learn from it.