Girls I need your advice on asking a girl I don't really know on a date?

Im 19 years old. I usually ask women that I've known for a while on a date. I've always wanted to ask a girl that i don't know on a date. There is this bank teller, i believe 19 or 20 years old, gorgeous and the night before I noticed her at the ice cream store that I was at with a friend. We both glanced at each other in the store when i walked by. Then I left. We don't really know each other, but I was thinking the next time if go to the bank to make a deposit Im going to start a conversation with her and then ask her to have lunch sometime. Girls, what do you think about this idea? any suggestions?