Actually their is quite a lot you can do about her resentment if you approach it the right way. AAs 12 steps are one of the best examples of restorative justice to be found anywhere.
The first thing to note, as others have said, she is not going to be that interested in words. She's heard it all before. She will be much more interested in an extended demonstration of the principles you are now learning to live by. Action, not words.
This means first and foremost working through those steps thoroughly and honestly. By the time we pass step five, we are promised, a major change will have begun to happen to us. By the time we have worked through steps 6-8 we will be ready in every respect to go out and repair the damage we have done.
At this point it is wisest to work closely with a sponsor and plan your approach. The person we wish to approach should also be ready to sit down with us. We can't just barge into their lives to save ourselves. This step isn't about us, it's about them. They will tells us what the amends should be and set the terms of any meeting.
With my ex, the terms were that I had to sit down with her whole family to make my amends.
What happened from that was amazing. I went to her to ask her forgiveness and what I could do to make amends. I admitted my faults to her and the family honestly recognising that I had been in the wrong and hurt her (contrition) I undertook never to behave that way again (repentance) and I offered amends an whatever form she thought appropriate (restitution).
The result was that she forgave me, freeing her of her resentment. This lead to a reconciliation and restoration, not of the original relationship, but of trust in each other. She and her family have been good friends of mine ever since. It was the most helping thing I have ever experienced, and it forms part of the promises around step 9 page 84.