Should I reach out to my ex girlfriend?

My (29m) ex girlfriend (32f) broke up with me six months ago. She was right to do it, I was immature and neglected our relationship, I really messed up. However she also said to give her a call when and if I ever "grew up".

I worked on myself and I think I learned from my mistakes and will never repeat them again, should I reach out to her? Common friends told me she's not seeing anyone at the moment and she still thinks about me, do I have a chance?

I feel so nervous, I screwed up with the most amazing girl in the world...

Should I reach out to my ex girlfriend?
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