Smile and talk to her. That is, scientifically, the approach that is most likely to work. It might not, though.
The alternative is to secretly stalk her to find out more about her and approach her "randomly" somewhere else. This approach is, however, very, very creepy. And not recommended. And probably illegal.
So just dress nice (but not too nice), smile, and try to strike up a conversation with her. You'll probably fail, but this is the best non-creepy non-illegal way to introduce yourself to her.