Unlike some people, I will try to help
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encouraging her openness, and even called her out on being shy which pushed her to open up more.
No, no and no! Shy people already know that they are shy and pointing it out will accomplish the exact opposite of what you are trying to do, which is opening her up. The way to do it (at least from my experience...) is to make them comfortable. Once they are comfortable around you, they will automatically become more open. Quote:
When I'm out, I'm almost tempted to just walk away from these girls who are being boring and closed off, and find people who are open and willing to have fun. Should I? I'd like to help warm people up, but how?
You should go for whatever you like. If I go out and meet girls for a short period of time I want them to be extroverted because that's fun! However, I often find that once shy girls open up, they are usually a lot more fun than extroverted girls! It's all about making them comfortable around you but that takes some time (which I'm not ready to invest in short term events such as a night out in a bar 
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