This is something that is better left unsaid. Think about it --- what purpose would it serve to tell your girlfriend? As you said, it would crush her. This is not to say that what happened was right---it isn't. You recognize that what you did was wrong and have made positive changes in your life so that you don't repeat this again. You also said that the other girl regrets her actions and it's highly unlikely that she will tell anyone.
So, let it go. If you are having problems letting go and feel that this is eating you up inside, then perhaps, you could consider getting counseling.