Well.... to start with... how long have you been friends and how long has it been since you've been trying to change?

If you have been rude and horrible to her for a long time or that, it WILL take a while to earn her forgiveness and to prove that you have changed. That doesn't happen overnight. And no matter what you do... or how genuine you are.... you can't rush that. It's unfortunately the product of your choices in the past. It is really hard to start accepting that someone is now being genuine when in the past they have been the exact opposite, so when they start acting that way.... well, you doubt it.

To use my brother as an example: my brother is a terrible person to me and my parents. My mom has been pretty bad too. My brother will act nice when he wants something in particular - his voice even changes when he starts to be manipulative. So... I shut it down instantly. Of course, then he gets pissed off with me because he was "just trying to be nice"... and that works for him because he is still coming out in his own head as the nice person and victim, which is what he wants. He'll keep going until it ends up that way anyway. There have probably been various times where he actually WAS sincere... but why or how would I believe that? There is no way to tell the difference.

Do you go to therapy? Do you have a diagnosis? If so... you could talk about those with her. You could explain what the issue actually is, and you could talk about the things you're working on with your therapist. That might help her with helping you to make adjustments and it might help her start to accept them.

But then.. it's always hard to heard bad things about yourselfs, and it really stinks that you're feeling so hurt. You may just have to continue going "I understand you feel that way, but this isn't helping either of us so can we start a new topic?" or something like that.