Slade -- well, I suppose some of the girls I know DID go looking for guys. Those are the girls who had boyfriends! Most of us, like me, just complained about it a lot. And we were not the hapapier for it! So, like a big hypocrite, I am suggesting you learn from my mistakes -- the ever popular do as I say, not as I do! Or did!
But don't pysch yourself out of it, either -- dead air in a conversation is normal, and as much as it is awkward, it will pass. Don't fear it, embrace it! Well, maybe that's going a little too far, but don't worry so much that the other person is freaking out and mentally writing you off because there's a bit of a tricky gap when you first start talking -- they're just worrying that you're thinking the same about them.