I was just about to post a thread about this. My spider just got the same treatment about twenty minutes ago. The bite wasn't quite as bad as yours, though. The mouse caught him on the neck and under the chin; it bled for a while, but stopped quickly. I rinsed it off with a damp paper towel and put some neosporin on it, and now I'm just hoping it doesn't get infected :/
I put him in a dark container with clean paper towels inside his cage; I won't leave him in there for very long, but I think it'll give the wound a chance to close up a bit before it has to go on his bedding, especially since it's under his chin.
Good luck with your little girl, hope it heals clean :]