If she agrees to talk you have to make sure that you don't allow the conversation to become a fight. For the most part, you will be able to set the tone. Don't get mad, don't bring up past issues, and don't point out what she did wrong.
When you meet prove to her that you are capable of accepting responsibility for your part in what went wrong. Own up to your mistakes and let her know what you plan to do things differently so they don't happen again.
Talk is cheap and there is a good chance she's heard it all before.
If you really want to show her you mean what you say, then show her you mean what you say! Walk the walk. If you can sit down with her and calmly discuss these issues without getting mad or defensive she might just see another side of you, and consider getting back together.
It's such a shame, but so many good relationships get ruined just because two people never really learn how to talk to each other. Sure, they can yell and scream and blame the other person, but they don't try to get to the root of the problem.
If you can learn to do that you have a good chance to get back your ex girlfriend.