Girl I have been seeing is scared to be with me due to S/H

I have known this girl for almost a decade. We went to high school together and remained somewhat friends after. We are both 23 this year, and started seeing each other around a year ago. We took a long break when I went back to finish school and she went travelling because we both had vowed to not do long distance without a more solid foundation first. Now, we are back in our hometown finally for an extended period of time. We have started seeing each other and talking again, and the other night I asked to make things official. She told me, while crying her eyes out, that she is terrified to be with me because of a past suicide attempt. She is so scared that if things end badly or if she messes up in some way, I will do something dumb. I don't know what to do. I am not the person I was when that attempt happened - I have put in so much work to change and grow and get better. But this just makes me feel fragile and like I am a burden who needs people to tip toe around them. It feels horrible. We both cried for hours about this. The thing is, as good as I am doing now, I cannot sit here and promise that I will never ever again be suicidal. If someone wants to be with me, they need to accept me flaws and all, right? BPD and my suicide attempt are part of who I am now. I can appreciate these inherently negative things because I like who i am now, and they have made me who I am. It sucks, and it hurts, and I don't know what to say to her - but part of me is realizing that if she can't make peace with this, she isn't the one for me and I am not the one for her.