Most girls enjoy outgoing guys. Some are attracted to shy guys out of nurturing instinct or such, but rarely does a girl look at a guy and get attracted because he's so shy.
Outgoing guys are in high demand because they're not intimidated by girls. They're fun to be around and not boring. It's easy to relax around someone who is confident.
There's a secret you may not know though... Girls are just like guys, except they have vaginas and like shiny things. They snort, spit, poo, fart, pick their nose and have just as many insecurities as guys - often many more so.
It doesn't matter how popular and beautiful a girl is, beneath the surface they're all the same aside from personality differences. Even a tough "I don't care" type girl will have many of the same worries and concerns a prissy socialite has.
Perhaps knowing this will help you be more outgoing with girls. You have nothing to lose. Girls are not magical beings.
You can research how to approach girls online and find some really good info. It's all about being assertive, open, direct and unafraid. Girls respond extremely favorably to confidence.
Try and put yourself in situations where you'll be surrounded by girls/women in a non threatening cooperative environment. Like a cooking class.
Sorry for the ramble, but I used to be shy before - until I realized it was the most useless thing in the world. It had been with me from my upbringing and it took a conscious change of mind to drop that frame of mind. So good luck