OP, my personality and situation is similar to yours, so I have a lot of sympathy. I co-sign everything Maegnus posted and add the following random thoughts.
Woman have certain security issues when it comes to dating that men do not have. A woman wants to know that a man she just met is not a psychopath or won't become one if things don't go well. Accordingly, they have their guard up and are easier to meet if you have something in common, be it a friend or interest. I would rank the following ways to meet women in order from best to worst:
1. Set-up by friends who know you well.
2. House party/happy hour hosted by common friend.
3. Happy hour centered around common interest/background (
e.g., alumni group, hobby).
4. Social happy hour not centered around common interest/background.
5. Bar/club on Friday/Saturday night.
1 and 2 are difficult if you have a limited social network. It sounds like 5 is a non-starter. Most meetups fall into category 4, which is why they've never worked for me. I recommend that you concentrate on category 3. Cooking classes are a good start. Do you like wine? The arts? Tons of single women at those events.
I'm not big on online dating. I think it encourages "checklist dating" whereby people (both men and women) reject potential partners if they are the "wrong" age, race, religion, height, profession, etc. Whereas if they actually met the person, they might hit it off. It's okay as a supplement. Ditto for events that are specifically geared toward singles. I've discovered that they attract lesser caliber singles. Of course, I occasionally attend those, so who am I to talk?

I am skeptical of PUA concepts working on the type of woman in whom you would be interested (presumably intelligent, professional women in their late 20s and early 30s). That said, PUA has contributed some valuable ideas like the "three-second rule" (walk up to and talk to an attractive woman within three seconds of seeing her). It's worth checking out, but take it with a mountain of salt.
If you're in good shape and dress well, you're ahead of the game. This is not StyleForum propaganda. Women notice these things.
In the end, it's a numbers game. Attractive women generally do not approach men, so you're going to have to suck it up and do the approaching. It never gets easy (if it does, you're probably approaching women you don't find all that attractive). Don't take rejection personally and don't be rude if a woman isn't interested. Just move on to the next one. If a woman is talking to you for 15 minutes and isn't looking for a way out, she's probably willing to go out with you. At a natural break in the conversation, say something like, "I've really enjoyed our conversation and would love to continue it sometime after work. What day and time work for you?"
Hope this helps. Good luck!
Edited by Ambulance Chaser - 3/19/13 at 1:48pm