Messed things up with my bestfriend

Hi, three years ago I met my flatmates girlfriend. We all moved in together and had been living together for 2 years. In this time he has cheated on her and she has found out and stayed with him. Me and her became really close friends and over the past couple of months have been really close. In the last year I developed feelings for her and revealed these about 3 months ago, it caused a lot of problems as there were other factors involved. She had needed some cash so joined a sex cam website which I accessed and saw a lot more of her than I ever imagined. She forgave me for this and it even brought us closer. In the last week she has broken up with here boyfriend and made the decision that she wanted to see if me and her could make things work. Within 20 hours I messed it up as she was convinced I only wanted here for sex, I admitted that it was something I wanted, but it wasn't the only reason I wanted to be with her. I have come to terms with the fact that we may never be together, but she was my bestfriend and I miss her. I had a long talk with her today and she is trying to decide whether she can give me another chance or not. I have been both the worst and best friend to her and I want her to give me that chance, the problem I have is proving to her that we can be friends again. If she makes the decision to give me another chance she has told me that there is only a limited window to prove that she means as much to me as she does. The problem is, I don't know how to prove it and hope that someone out there can give me some advice on what I should do.

Prove it to her by taking her out on real dates and not having sex afterwards. Genuinely talk to her and ask her questions you may not know about her. Soon she will realize you like her for her