Gotta start slow man... I'm totally like you in that I've always abhorred cold approaching. I'd never approach a girl unless I knew there was at least some IOIs. That being said I'd always say hi to girls even if I didn't take things further w/ approaching, etc.
Deadly ripped gave you some money advice for developing confidence in approaching, etc. I'm gonna go one step further and suggest that you expand this to lotsa people in general, and not just girls. A big part of getting the "game" is to have good socio-sexual awareness.... yes I did make that word up. I basically mean that you need to be aware of the kinds of energy/vide that people are exuding. Its an invaluable skill to have in social situations because it allows you to gauge a girls' interest in you with out any kind of contact. It takes a while to develop, but man its almost like having an extra sense once you master it!! The way you master this skill is to interact with tons of people in many different social situations and get a feel for the energy that different people radiate.
Remember to be confident as well. Women can smell fear. Getting jacked and staying lean are in my opinion, the easiest and most effective ways to get crazy confidence while simultaneously have women drooling over you. There are also tons of additional health benefits. Trust me on this, I was a stripper for 3.5 years... I've made tens of thousands of dollars off my build/looks and can attest to this first hand. When you're in top line shape all you gotta do is walk down the street in a tank top and you'll have most people (girls AND guys) checking you out. The proportion of women that'll be interested in you will be high. Life is A LOT easier when the girl is intrinsically attracted to you, because all you really gotta do is not phuck it up. If you're in elite shape and have the "bad boy" label a lot of girls will actually want you JUST for sex (again, I speak from personal experience)... not sure if you're into that or not.
Another strategy I like to use is "stalking" ... no don't actually go out stalk women!!!! Its illegal and dam creepy! By stalking I mean more you build sexual tension/attraction with your target, build rapport, get her comfortable with you, etc... By the time you get a date and get her back to your place she's begging to have your cackn'balls.... When you use this strategy with girls that are into you then you won't have to approach very many women, and you'll have a relatively high success percentage.
Keep plugging away man.