Meeting girls as an introvert?

I'm really introverted, and as much as I've tried to be more social I really don't enjoy it most of the time. I'm 20 and I've only had one girlfriend and she pretty much fell into my lap and did the pursuing.

I'm not particularly shy but I have poor self esteem, so signing up to a dating site would probably depress me if I didn't get any replies. I've had girls express interest in me in the past while out drinking, but in all honesty I don't enjoy going to bars and just talking to friends because most of the time I genuinely don't care what they have to say and feign interest to be polite.

I feel like I have the mentality of a grumpy old man at a young age, I've made efforts to change this but I guess it's just who I am.

Is there anyway to meet girls outside of bars/clubs etc without risking my fragile self esteem?