Re establishing trust

So Ive posted here before about a girl ive known for 10 years and I getting involved after she broke up with a friend of mine. Her and I had a lengthy romantic/sexual past before her breakup. After the breakup she came to me and we got together. Things were great for 2 months then she pulled back and didnt say why. After a little time apart she came around and told me why.

One night her and I were drinking together. I was way drunker than her. I apparently was acting too aggrressive for her tastes. Keep in mind her ex is a full on alcoholic and her dad had issues with it too. So up until that point things were great but she said that one night really scared her. she was scared of repeating past mistakes. She also said she lost some trust in me. Actually a lot. She reiterated she has strong feelings for me and isnt seeing anyone at the moment. She said she wants us to hang out as friends and see how it goes. I told her how much I wanted us to work and how happy we made each other. She agreed. She said our relationship was great. but this one incident really made her pull away. She also saw me drunk again since then and wondered if its the same thing all over again. I told her im not that guy and I wouldnt do it and she said shes heard that before. of course it wasnt from me, it was from someone else. I can say 100% it was an isolated incident, an off night. I told her I could cut back and she said she doesnt want a relationship with those types of qualifiers.

So now she said its gonna take awhile for her to get that trust back. She was adamant that hanging out with friends and seeing where it goes is what she wants. I know shes hanging out with other guys but isnt doing anything with them (so she says). I know her well enough to know she isnt a BSer. Yet there are guys around her who like her. Shes going on a group vacation this week with some coworkers and this one guy whos into her will be there. There isnt a damn thing I can do about it.

So I dont know what i can do to prove to her im not that guy. Id like to be her friend but we clearly have gone deeper than being just friends. I basically am gonna have to sit there and watch her hang out with other guys and wonder if/when she'll come back around. i asked her if theres anything I can do she said "I wish I knew, it would make the questions Im asking myself a lot easier."

So is there anything I can do besides wait it out and be friendly without pushing boundaries?