LGBT: Should you apologize for being awkward when coming out?

If she's also a lesbian, she probably understands that it is a really nerve-wracking experience to come out. It's normal to be that nervous. I think she would understand, but you could explain what was going through your head, and maybe talk to her about her coming out experience and see if she has any tips about coming out to your parents. (This is assuming she's totally out of the closet, by the way.)