i think you gotta find some good pretexts to see here a couple of times more before making any move. Is she just a teller or does she have some, anything to do with investment, credit card advice blah blah, if so you can prolong your tet a tet with some "investment" chit chat and get a little more personal. I am not suggesting you take your sweet time, but knowing someone longer, even if that means just exchanging a few hi's and how are you's, and some trivial chit chat, it always helps to break the ice, to be more familiar, that does matter to women, a woman might fancy you but being too up front can scare one away.
I d discard the note or flower strategy, both of them are way too banal and innefective as well, flowers seems too agressive a way to go, since you really just fancy her, and as don rightly said, flowers are more of romance thing for woman, and might seem a bit too abrupt to a complete stranger.
Also, try to size her up. Some women like men to be more up front, others not. I know that trying to conjure up some psychological profile of a girl you really fancy can be a hard thing to do, but it always helps me when i get a better idea of who i am dealing with, you crack a joke and sense she likes it you go along that way, you say another thing and you notice it's not sinking in, you try something different.
Chat up lines are boring, and film materials.
Bottom line, i d find some good pretext to go and see her a couple of times more, try to start up a few brief and trivial, but personal, chit chat, maybe have a friend call you when you are there on the cellular and say something personal about yourself, not bragging or anything just something that d make you seem more intimate to her, or say something you then feed back into some conversation with her. And then after a couple of times, you can tentatively try to make some smooth transition from the trivial chit chat to asking her out, say you are talking about your car breaking down, and you go, as much as i like driving i wouldn't mind you giving me a lift and then i can get us some coffe/dinner blah, blah, if you cannot make the transition smoothly, just ask her out with any line that comes to mind, women appreciate when someone's interested in them, and usually say yes.