Quick tip: I've never meet a girl that doesn't like to dance. Plus, being a girl, I know that fact is true...
Maybe you could try to take a dance class like salsa or swing or whatever you think you'd like. In a class, when you're learning to dance, you're kinda busy learning so you have less time to wonder if you're looking/acting stupid. Plus, everybody else is also learning and making mistakes, so you won't look like a fool more than anyone else. You also get to make small talk with the person you're dancing with. Also, you learn to place you're hands at the appropriate places, so you know you'll never offend a lady again (well, unless she wants to, but that a different story...
). And to be honest, for my part, I really don't care if the guy I dance with isn't that good, as long as he's making me twist and turn and I'm having a good time (and him also), that's all that counts!
If dance is really not your thing, try to find a group of interest to join (like toastmasters, the red-cross or anything really) where you can meet people and do something you like. For example, a couples years back, I was also involved in providing first aid at events through a organisation like the red-cross. It gave me the opportunity to meet a lot of people.