Honestly, you messed up, but I am sure you know this.
Give him a break. Count off ten days and don't talk to him, don't look at him and when he talks to you, just be very polite but to the point. Seem a bit sad in front of him.
After ten days (now, don't dress up for this, just go in sweatpants and don't wear makeup) knock on his room's door and tiredly say "hey, could we just forget about what happened? I'm really sorry about my behavior, I was drunk and I don't want you to be angry at me forever because i *****ed up on one night". And wait for the response. As easy as that.
He'll surely forgive you. If you don't dress up for the apology but look great for the ten days otherwise it'll be evident to him that you aren't trying to get him and you just want to stay friends.
GOod luck