Search Results: starting a conversation with a girl

So I work the front desk at a gym. One of my responsibilities is to greet people and sign in members. There is this one girl who comes in regularly, and she is absolutely drop-dead gorgeous. I end up greeting everyone, and half the time people just ignore me, but she always comes in with a smile. Typically I would just chalk this up as being polite and think nothing more of it. Yet when she leaves after her workout, she always makes a point to stop at the desk and say bye, even if I'm distracted or busy working on something. Also, right before Christmas break (I'm assuming she left because I didn't see her for a while), she was walking by to leave, yet before she could say goodbye, a coworker came over and started discussing something with me that we needed to do. As I was listening to my coworker, I caught a glimpse of her lingering by the door and looking back with an almost sad expression on her face.

I keep trying to think up some way of casually starting a conversation with her, but I haven't had any luck yet. Do you think that she might be interested, or am I just letting my wishful thinking go wild? Also, do you have any ideas of how I could start a conversation with her?