Whether or not you actually met the girl, the fact that you intended to, and kept it hidden from your girlfriend, means you screwed up. Once you admit that, and truly apologize, you can start working to make things better.
It is good that you are willing to make up for it, but you need to give her time to cope with the situation. Imagine if you were in her situation--it would probably take you a lot more than a week and a half to deal with it. She has the right to be upset right now. Give her some space, give her some more time, let her do what she needs to in order to come to terms with what happened.
John, I don't mean to sound like you are a bad guy or that you deserve her coldness, so please don't take it that way. I'm glad that you are willing to make things right with your girl, because I know so many other guys out there simply wouldn't care. But infidelity, and even just the prospect of it, is a very big issue that takes time to resolve. Don't smother her with apologies and demand that she talk to you about it, just do your best to make sure she knows that you are still committed to her. She'll come around, and things will work out. I wish you the best, and please keep us updated on your situation.