As I've told many, many other people there is nothing you can do to change how she feels or what she thinks, no matter how hard you try. The act of trying itself proves nothing and makes it seem that you haven't changed. The only way she would know if you changed is that if she wanted to. However, your past has just proven you to be a failure and that will not be something she will forget about. You will forever be associated with that.
I am the better person I am today because of my ex too. Imagine me being 23 years old before I fell in love for the first time and got a serious wake up call. If I had just gotten this earlier I wouldn't be in the position I am now. But the fact that if you truly changed, it will be noticeable to those that have know you for a while. It's in how you act, it's in how you talk.
I know you care about her man, but you have to stop letting her know that because it will be you seemingly clinging to scraps of the relationship that failed before. You have to stop checking in on her because it will seem you have nothing better to do than keep tabs on her. Part of that driving force, your motivation to do these things are because you want redemption. I'm sure you want to resurrect any feelings she had with you from before too if they are deep down there but it's just getting you farther from want you want with her.
Guys always make the mistake of trying too hard. It never works and won't work for you either. If you were to ever have a future with her, you would both need to put what happened behind you, something easier said than done. To start something new, not get back together. I would advise talking about the past too because it is just bringing back the hurt that you guys went through.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.