White Female, Asian Man Dating Advice?

I hate it that I can't get this guy out of my mind, it's like a drug. He's been checking me out at the gym for a couple of months. I'm talking straight-up, obvious staring. I've been checking him out too, okay, because he is sizzling hot. But he won't approach me, and I won't approach him because I get clumsy, petrified, and tongue-tied. I walked right up to him and told him my name one day and shook his hand and then practically ran away from him because I was so nervous. He looks like he is between 26-31 and not in America for very long due to heavy accent. Yesterday I gave him my phone number on a piece of paper while he was on the elliptical (it's been eight weeks of nothing but stares.) Maybe that was too forward. But how long can the ogling continue before an escalation in communication occurs? Driving me crazy! I want to have conversation. I like education. I like different cultures. I love the Orient. I like Asian man. Was this act too forward?