STAY OUT OF BARS!! The whole atmosphere in those places is so yucky that an introverted guy is going to feel overwhelmed. I won't go into the type of people you'll meet in a bar. Sure, some of them are nice folks, just like you. And many of them are the scum of the earth, and how the hell do you tell the difference when the music's so loud, the air is so smoky, and you've got a couple of drinks in you.
When I was single some years back, I found a church that sponsered a nondenominational singles group, that was built around a weekly evening program, followed by some of the group adjourning to a local pub. On weekends there were group sponsered social activities; rafting, house parties, hiking, etc.
Groups such as this offer a low pressure way to encounter new folks in general, not just potential dates. I made far more "pals", both male and female, than I found women to date, but those I did end up dating were people I'd had met and experienced in general social ways before I ever thought about asking them out.
See if you can find such a group where you are. I promise you, meeting folks in such a way is a lot less stressful than hanging out in bars.
Oh yeah, almost forgot---Parents Without Partners is a good way to meet new folks. If you're anywhere near a metropolitan area, there's bound to be a chapter around. Check the phone book.[:D]