Should I just add her on fb ?

I don't think a Facebook friend request is a good first contact. A Facebook message would be good (if her privacy settings allow), or you can arrange to meet her somewhere. It doesn't have to be between her house and her car. Since you have a mutual friend you know some of her interests, if you share some of those interests go to where that thing takes place (this sentence is starting to feel like algebra) and introduce yourself there.