How do I show her I've changed?

Me and my ex girlfriend broke up about 2 months ago. I've just recently met her for the first time after the break up. Everything went surprisingly well, we got on just as well as we used to, not awkward at all and it's like we hadn't been away. She brought our relationship up and we basically spoke about what went wrong... I told her that I was sorry for what I did wrong, that I was immature and didn't mean to hurt her feelings when I genuinely didn't, I love her to bits...

Anyway she is saying part of her wants me back and wana to sort this out because she loves me, but the other half doesn't because she's heard me say it'd be different next time and she's struggling to believe it... I really want her back but to he honest I can't show her it's different and I'm different without being with her...

Any advice, thanks in advance