Here's that question

I'm the yin to Carlos' yang .....
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Yes strike up casual conversation but I wouldn't hand the card...Carlos' suggestion works, it just seems natural to talk to someone who's stand in a line with you.....
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If you've noticed her, she's likely noticed you...Maybe get in line behind her and say something to make her chuckle ... like "it's terrible this addiction I have to this place, I don't even like coffee ... and i'm getting tired of making paper mache with these things (holding the paper) ... (she'll laugh) ... you smile and say ... oh i've seen that smile before you work in my bldg. (she'll blush) ... can i walk you back? ..
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Angie..

Angie's my princess.....
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How about next time you see her buying coffee get right behind her and say a few words to break the ice like ... what a beautiful day outside, sucks to be working". Tailor your next line to her response , if she says more than a word or two you've got a conversation, if she just smiles, at least you've broken the ice for the next time around...
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Whatever you do don't get to chummy cuz the last thing you want is to be classified as just a friend. At some point make a move by actually asking her out for coffee, or since she's in the building make a date during the fay to meet. This will test her perception of your relationship...
Much Luck Bro...
C...

I agree with Cargie (that's my new celebrity hybrid name for Carlos and Angie, don'tcha love it?) that if possible, you should try to start a conversation with this alluring stranger. That would at least give you a smidgen of foundation from which to start. However, I wouldn't rule out just handing over the card with a smile and a "call me" or "I'd love to take you out for a drink." That puts you in the position of alluring stranger, ergo giving you an edge. I would be very flattered and intrigued if a clean-cut guy in a suit approached me that way..(as opposed to the filthy homeless chaps who usually approach me). I would probably call and go out wth him just for the novelty and fun of it. I realize I'm not the typical woman -- but what have you got to lose? She says no and doesn't go out with you? She's not going out with you now, so no harm, no foul. Good luck! And wear a red tie...

Not sketchy. I met a cute guy on an elevator leaving the courthouse once (he was an attorney and I'm a journalist) we ended up going to lunch together that day (it was lunch time, we were both on our way to grab a bite, so we went together). And then we went on a date that weekend...
Why not just start with "Hi" next time you're on an elevator together, or getting a coffee. Introduce yourself, chat a bit, and maybe ask her to lunch...

Next time you see her in line for coffee, offer to buy her a cup...Most girls are flattered by chivalry, so I'm sure this will make it easier to talk to her...Even just a short chat or "hi" when you see her will pique her interest as well...Go for it, and good luck :)..