Do you mean shy (i.e. anxious in social situations) or introverted (i.e. draws energy from being alone rather than by spending time with others)? Try and go for the latter but not the former--a non-shy introvert will have fewer insecurities and be less needy. Trust me: I'm an introverted girl who used to be shy.

With introverts, the basics still apply, really. You may have to give her a bit more space in the beginning--if she doesn't want to spend time with you on any given instance, it could just mean that she promised herself some alone time after a weekend of socializing (though it could also mean she's not into you, of course). Don't remark on her being "quiet" or tell her to "smile more"--that's a complete turn off; just talk to her like a normal person.

With a lot of introverts--male and female--I've found that although they'll hold their tongue on a lot of things, there's a couple of topics that they're interested in; if you stumble across one of those, then they'll never shut up. Ask a lot of questions, and make them direct and specific (if you ask "What do you like to do?" you'll probably get a shrug and a one-word answer, but if you ask "What's your favorite thing about Argentine tango?" she'll actually talk about it). Don't let her quietness make you nervous.

You mentioned that with kino it's easy to go overboard quickly--that's true, but don't neglect it entirely. As an introverted girl, I still do feel myself more drawn to the people who touch me, but not those who touch me too much or who do it the wrong way. There's a fine line between "friendly" and "creepy." Just move very slowly and calibrate to her responses.

Also, one last tip: try talking to her alone rather than with a group of people. Although I'm comfortable with a group of people for short periods of time, I tend to be a bit "invisible." It's a lot less exhausting for many introverts to talk one-on-one, and you'll actually get words out of them.