getting/having a girlfriend actually played a huge part in me overcoming a big chunk of my anxiety.
It's really not that hard to meet people of the opposite sex who share your problem, or will be understanding of your problem. Dating sites make it easy. Just use the keyword search feature and type in 'shy' etc. Although most girls/guys wont disclose their insecurities, so you just gotta get good at picking up on those certain vibes.
Forcing yourself out the door to meet the person will certainly be the most difficult part. I'm extremely selective in who I'll meet as I'm always really afraid of rejection or some type of dating disaster. So I like to make sure the girl is 100% into me first, and is on the same page as myself in terms of shyness etc.
Once you do it and have that positive experience, it'll get a lot easier and you'll be less anxious about it in the future.
Having a boyfriend/girlfriend can sometimes be the single most effective way at overcoming your anxiety. Dating forces you to hide your insecurities and get some confidence. It's a great feeling.