The other day I went to the bank with my parents (because I had to transfer a large sum of money and didn't have all the stuff I needed to get the job done, so it wasn't for a reason for which I'd usually go alone).

Anyway, I see some beautiful girl who serves me/works with me to do what I need but obviously didn't try to make any conversation outside of "business" due to being with parents (and I could have made all sorts of comments).

Out of boredom, I decided to enter her name into FB and see what comes up. Her profile comes up (the pictures look the same as her) and, funnily enough, we share a few of my uni friends (those friends I don't really see at all, we're not that close). I'm not at uni anymore btw...

Would it be wierd if I used FB to send a msg to her? It's a shame because FB doesn't really help in making new friends like this (if the idea is bad, and it does have its problems). This sort of thing would usually be seen as creepy. What would be a good type of sample message to send? I ask as I have very little creativity in this area of my life and if I come across as creepy, I have no chance at all. I also don't know if she is single or whatever.

she might think its creepy but if you do a good job of taking the edge off of it with some tasteful humor and mystery then she might throw that aside and give you a shot.

Unless you're brilliant at online communication, sending her a message on Facebook will come off as creepy/stalkerish. Find an excuse to go back into the bank without your parents - ask about a new account, anything. While you're there, ask her if she went to the same university as she looks familiar. You can then start talking about mutual friends and take it from there.