Any tips to get over the shyness I have with girls?

I'm a very introverted guy usually, but with people of the same sex I'm usually a bit better but you can still tell I'm a bit introverted. I am apparently quite attractive though, as a lot of girls have called me cute and hot but just my shyness is getting in the way. The worst is there's been a few times when girls came up in a nightclub and asked me if I was gay because apparently they've been hitting on me all night and I didn't even realize it.

Well, I've been doing my best to talk to girls but the progress is slow and arduous. Now the problem is there's this one girl I really like at the moment, she smiles a lot at me and when we greet she would hold that smile for a lot longer than she would to other people and maintain eye contact even after I've already smiled back and said hi. She made some small talk about neutral stuff like what I was doing for holidays, or like whether I've just been outside if it's a good day or if I'm going outside later. I want to try and befriend her since we seem to be just being nice to each other because of one of my best friend is a mutual friend. The thing is as soon as my mutual friend is there I tend to regress into my little personal bubble and don't try and talk to her directly as much, but as soon as my mutual friend is not there I'm more able to smile and maybe even talk a little bit to her and it seems the same for her too. She wouldn't talk to me if the mutual friend is there, but she would make small talk with me if he wasn't there. Anyway to break the ice a bit more and so she's comfortable to talking to me? or even better anyway to make me more comfortable with talking to her? I've only ever managed to befriend one girl I liked and that was because she initiated conversations with me a lot (almost every time we saw each other) so I felt comfortable to initiate conversations with her after a while.
Any tips to get over the shyness I have with girls?
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