I'm a girl, so here is a female opinion!
First of all, I think you should work really hard for awhile to show her that you really are changing and you really do have the willpower to keep at it.
Since it has already been a few months since you confessed, it won't be so daunting to her if you approach again in a month or two, but like >>6 said, you shouldn't really confess, especially since she's rejected you before.
Ask her out for coffee or something simple like that, and try to be nonchalant about it.
If she says yes, then great!
If she says no, I would do one of two things--
1) Pull up a TON of confidence, and try and convince her to give you a chance. Say something to the effect of: "Just give me one shot. If you don't want to go out with me again, I'll give up and leave you alone about it, but please come with me once just to try it out!" See what she says. Putting it that way makes you sound confident without being cocky.
or 2) If you really feel like you'll have no chance with her, ask her what she doesn't like about you. Even though it'll be hard to hear that, it will give you a list of things you can work on so you can come across as more desirable to girls in the future!
If she rejects you a second time, then I wouldn't really ask again. Some girls might like that, but i think most would feel annoyed/creeped out after too many attempts.

Keep us updated, and good luck!!