Well... I was probably like you are, or perhaps worse. In high school, I was not only shy with girls, but I was becoming someone withdrawn, and I decided to overcome it. I joined the school choir, and was very nervous the few times that I had to sing in public (with the group). After a few years of getting in front of people I began to get the confidence to sing solo. It took a while, but I was able to go in front of large audiences and sing without falling to pieces.
Later on in college, I pushed myself into public speaking a bit. This helped a lot when I ended up in the workforce. When I landed a job, I took the opportunity to present to colleagues and at functions. This further built my confidence and today I present at conferences and to high level executives around the world.
That never did help with my shyness with women. I think I still lack confidence there, but luckily, I sort of put women on the back burner through college, and then I met my wife at my first job after college. We worked on a friendship for about a month before I got up the courage to give her a kiss, and worked on that for another 2 months before we got serious. Three years later, we got married.
So... if you want to meet someone that's right for you, I don't think the shyness will stop you from finding true love. I was 23 when I met my wife, and I see a lot of young folks these days who are not shy when it comes to the opposite sex, and yet they just keep going from one meaningless realationship to another.
On the other hand, if you really want to overcome the shyness with women, I would try something similar to what I did with singing and public speaking. The only way to overcome your anxiety is to make it less threatening. To do that, you have to put yourself in that situation many times to get used to it. I always recommend to folks who are looking for a job to go on a lot of interviews for jobs they don't really want. They won't care if they don't get a call back, and it gives them some perspective as to what employers will ask and gives them a chance to polish their responses. I would say the same is true in your situation.
If you really want to overcome the shyness, go out with a lot of women in whom you really have no interest. Maybe one of those 5 minute dating things would be interesting. In the Boston area, there is something called "lunch dates" where folks just meet for friendship and lunch. Also, internet dating might not be a bad choice. The trick is to just meet some women as friends, get to know what you want to talk about, and what they want to talk about. Don't care if you'll ever see them again... and this will help you overcome any social anxiety. Then you'll be ready to talk to the women you do want to date.
Truth be told, if the woman is right for you, it really won't matter, but these tricks might help you boost your self confidence. -- Good luck.