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Flirt with her. Tell her "There's my favorite passenger." Find out her name. Tell her yours. Get on a name calling basis with her. Find out where she is going, like is it for work or school, or home or whatever. Even only one or two sentence per encounter, that builds up over time and you can really establish good rapport with someone.
I would strongly advise against the note. It's creepy, it telegraphs intent, its inappropriate for a person in your line of work to do that. I mean what's she going to do, write you a note back?! It's just not a good idea.
10 thumbs up for this one - excellent advice. It would have been exactly how I would have responded to your post. Find out her name if you can - and then use it every time you see her. People love hearing their name and it gets their attention. Give her a compliment or two without sounding creepy or desperate - i.e. with a litle bit of enthusiasm "Theirs Julie - my favourite customer" or "You look nice today Julie" etc etc. YOu will soon be able to read if she is interested or not. Wont be too hard to figure out.
Down the track after you start talking to her, try and find out what her interests are - ask her what she has planned for the weekend (when it is close to the weekend). Then you can probably gauge if you are well suited as well i.e. if what she does during the weekend is going to the opera and painting pictures and what you do is go to football games and to the pub then you will probably lose interest in her as you realise you are complete opposites.
You only have a limited time to work with so you will have to take action sooner rather than later. Good luck - I hope it all goes well for you.