I'm a pathetic cheater..?

I cheated on my girlfriend after 6.5 years and we have been apart for about 7 months now. I am currently 31. I always believed she would be my wife, yet there were some issues. We got along perfectly, that wasn't the issue, the issue was after about 5 years in the relationship I didn't feel like it was moving forward. I proposed to her and she didn't accept because she felt to young(24). She also was so busy with work and school she had no time for me and I was lonely in the relationship. So yes, I made the horrible decision of engaging in another relationship. I was caught after about a week and continued it for a few months because I felt I crossed the line and there was no going back. When it that relationship ended, I realized what I did and what I had to do to make ammends. So I have been talking to my ex for the last month and a half. Mostly text and email because she didn't want to see me. We ended up seeing each other 3 out of the last 7 days which was really nice. I know: she loves me, she misses, me, she wants to be with me, yet she is still hurt and is rightfully having a hard time forgiving. Almost everyday she says we should try to stop talking or not see each other anymore, but shortly after she continues to communicate with me. I have taken ownership of my actions and admitted my faults. I have said I will go to therapy with her and do a multitude of other things to improve the relationship. I am looking for insight of similar expiriences. What works? What are my next steps? How much time will it take for her to move forward with me? Is it a good sign that she is willing to see me now? Would she have seen me if she wasn't interested? Thanks so much!