I think that would have been your best bet. Did you add a message when you friend requested her? The alternate option on the fb route would have been to send her a message (asking about the final) without friending her. And then if she responded you could have friended her then because you wouldn't seem like such a random. It's never a good idea to attempt to friend a girl you've never spoken to. It's just a bad way to start off the relationship. It says to the girl that you're into her but too afraid to actually speak to her. Also, if she's pretty, she gets requests from strangers all the time and if she's smart she just deletes them instantly.
Damn, whatever theirs a shitload of other girls that willl add u man. so forget this chick and move on