Wow, you have amazing trust and seem VERY mature! I would freak out from jealousy alone. Just something about issues I have had with past boyfriends has made me feel that ANY close relationship between a man and a woman, especially if one is interested, is not good. I see an intimate relationship like that as cheating as much as messing around. Even though DH has never betrayed my trust and I know wouldn't do anything to risk our relationship, I would not let him have that kind of friendship with a woman. That may not be fair but I have been burned too many times in the past, and even let things like that happen with male "friends" of mine.
It is really good though that you are being mature about it and showing this girl that you aren't intimidated by her and that you are very real and very serious with your BF. That is probably the best way to keep her from persuing him. I could never do what you are doing and I tip my hat to you, but also say....be careful.
I think meeting you was a good idea and an act of faith on your and your boyfriend's part. I'm not sure I could be as cool as you are but kudos on having such a secure and trusting relationship.
I am also so amazed at your trust in your boyfriend. You guys must have a very secure awesome relationship. I, like the otheres who posted could never imagine letting my boyfriedn have that kind of relationship. I wish I was secure like you!!