I think you need to show her by your actions that you're sorry.
Telling her she should or needs to forgive you....won't work. Have you gone out on dates at all?
Honestly the littlest things can mean the most. A phone call to check on her. Actions. It's all about your actions and she will be judging them. All of them. Hang in there.
BTW "what can I do to show her I deserve to be forgiven?" kind of bugs me. Why do you deserve to be forgiven?
Show her.
....Understand, that I can't, not be what I am I'm not the milk, and Cheerios in your spoon ~ Avril Lavigne ~ ..."Nobody's Fool"...
