Advice?

So my cousin now hates me. We where at a party in the weekend and she asked her ex to come with us as they are still good friends. Only we both had a bit to much to drink and I slept with him. I know it was a really shit thing to do. I told her what happened as I don't like keeping things from her. But she hates me now.

Any advice on what I could do to try and mend our relationship?