I usually either wait until someone asks me out or become friends with them, and work my way from there, etc.
I don't like rejection either, that's one of the reasons why I don't look at people or speak much when I first meet them, incase they don't like me, and then it goes worse, etc, etc.
Like, once I girl just came talking to me, and my head was faced 45* away and I was staring at a wall and speaking back normally, suppose that looked pretty creepy anyway, so I can't win, the furthest I've got with a proper focus is probably under someone's eye.
I doubt this really helps me get many girls, even though I've had an ok number, but really, if a girl thinks I'm a fucking weirdo for not being able to look at people, then they can fuck off, who'd want a girlfriend like that.