I hate to say this, but for a short while at least, you should back off. If pushed, she will just go further away. If you allow her some space and time to distance her self from the situation and let her emotions settle, it is more likely you will get an opportunity to rectify things. It is very hard to do this, but relationships are not easy.
The second thing is to try to remain humble about it. This might sound crazy, but if you try and try and get nothing, you might start to feel resentful. Then when she comes to you or is willing to talk to you, if you are resentful, you might blow the whole thing again.
Also, if you are really hurt by the situation, regardless of who caused it, please please please take time for yourself. Do something you really enjoy. Try to get your mind off the situtation, because I can tell you from experience, you probably aren’t thinking clearly either.
You might feel panicked, and feel like you have to do SOMETHING. That, in my experience, is a mistake. Continue to be the person you have always been, and be ready when the opportunity presents itself. If you get too neurotic (which is human nature, by the way) about the whole thing, you will just drive her away.
Finally, it is only your responsibility to admit you did something wrong and ask to be forgiven. While you want your friend back, it is ultimately her decision, and you can’t be responsible for her actions or reactions. She has the right to her decision, but if she is the kind of person you really want for a long-term friend, it is likely she will eventually come around.
Hang in there. Things seem bad now, but they WILL get better.