I always used to be the one that sat in the corner/bar of the club saying I'm going to approach, that girl. But when i actually had to I always made an excuse not to. At about 2AM when I'm about to leave i would manage to approach a girl, unconfidently, and get rejected, but I still always felt good that i had at least tried one girl.
As it progressed I could approach a bit more, but still unconfidently, and get rejected, due to being unconfident. When i got rejected i started saying "Your loss." and it actually helped my approach and confidence. It makes you feel like you have absolutely as it is, "their loss".
I have actually closed a few sets due to the confidence its given me over time. If you were like me, try it. There's nothing to lose.

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“If you can't ignore an insult, top it; if you can't top it, laugh it off; and if you can't laugh it off, it's probably deserved." - J. Russel Lynnes