Is it inappropriate to introduce yourself to a girl at the gym?

[sildottz]

I'm 21. There's a pretty girl my age at the gym. I've seen her several times (half a dozen), and we make eye contact each time- sometimes prolonged, sometimes brief. She's got her ear buds/iPod in all the time (she's either shy, or flat out not into making friends at the gym). As such, I'm apprehensive to disturb her during her workout just to say hi. At the same time, I feel like she's hoping that I open conversation. By now, she probably thinks I'm either a wuss, or a creeper.
I'm also unsure as to whether or not it's inappropriate or strange to approach a girl at the gym? Is it disrespectful toward the establishment?
What would you do? And girls, how would you feel? Is it bad to use the gym as a social meeting ground?
Thanks