Look, you were drinking and acted like an asshole (now whether that was justified or not it ain't for me to say). Having a few too many and launching into a tirade happens to *a lot* of us. Just remember gay, straight, bi, ect... We're all humans and subject to all of the vices that are inherent to that condition. We all make mistakes, we all will eventually express or act upon some kind of ignorance. I know it's cliched but really try not to be too hard on yourself. You had a less than stellar experience there, but it seems you've recognized the mistakes. Use this brouhaha as a chance to learn something about her and yourself, which can make for some very fertile soil to allow some growth in the interpersonal relationship you have with this woman.

Trust me, just calmly communicate with her when the time feels right and keep ya chin up. It'll all be okay.