How should I handle this girl if she comes back to school next year?

We have some major beef that I am going to very briefly summarize. We both romantically liked each other for 3 years. I got the nerve to say something and chickened out and said but it’s ok because I just like you as a friend now. (Lesbians hitting on their friends they think are straight are socially awkward). I invited her to a party she brought her new boyfriend he’s a fat commie(literally). I said congrats and asked her what I could do better next time and she awkwardly said over text I liked you to. Months later I asked if she’s like to give it a go in the future over text because I’m an idiot. I also tried to portray myself as a womanizer because I thought it would make her more comfortable with her choice of dating the other guy because I wanted her to be happy. She said no I lit her up pretty badly because honestly she wasn’t taking her health seriously and kinda deserved it because she treated both me and this guy horribly and used people. I later gave a whole hearted apology with a hand written letter and apologized with literally everything I have. She never responded. Just stares in public and now I hear wants to come back to our school. Which makes no sense because her friend group has fallen apart. She’s been at another high school for three years. I am willing to sit and talk about what happened. But how should I act if she comes back should I just ignore her? Or give a polite hi?