First and foremost, sometimes things happen and like your friend said you shouldn’t beat yourself up over it. I think a genuine, heartfelt apology would have to suffice for now until you have another opportunity to offer your services. I don’t know your friend so I can’t speak on her behalf, but speaking for myself, I wouldn’t let something like that upset me (unless it happens frequently, which doesn’t seem to be the case here), so don’t assume that she must upset and just isn’t showing it. I think you’ve done all you could do to show her how sorry you are and she seems to be fine with it so, again, don’t beat yourself up over it. You sound like a good friend despite what happened in this situation.