Well Steve this really depends on things. Have you done anything thus far that might make her feel uncomfortable or feel that she is being watched. Because whatever you do you can't risk making her feel that way.

Assuming this is not so then I do feel that a plant would be a nice gesture. It is also a great way to initiate conversation. You might even do so before you get the plant. You could let her know you'd like to do so and ask for her input in what would best be appropriate and what she would appreciate. What a marvelous way to open up a dialogue with her. There are ways this can be done without making her feel all creepy.

(BTW, your post put a big smile on my face. There are certainly worse predicaments one could be in, eh? I defintely will be checking back.)