Don't ask her out in an official capacity. Make it seem really casual. Like tell her you are bored and hungry and see if she wants to go get some icecream with you.

Aside from that, don't worry about taking her out anywhere. Just escalate whenever and wherever you are with her--whether it's studying or playing sports with her. Start teasing her or saying things in which she'll have to respond in a certain way, then push her, grab her, or hit her when she responds. If done playfully she'll be forced to laugh. Now you guys are having a good time together laughing and being physical. Then the next time you do something physical, it won't seem awkward or forced...especially when it's a little more physical than the last time. Eventually you start bear hugging her, or putting your arm around her and pulling her into you. Basically treat her like she is your play thing. Don't worry, she'll either give you ioi's or iod's to let you know if she'll tolerate it or not. If she gives you iod's freeze her out. If she gives you ioi's, proceed.

Once you have established a relationship of physical contact with the girl, by the time you start going out on dates it'll be completely natural to hold her hand, hug her, put your arm around her, etc. You have to pave the road before you can travel down it. Playful kino is the groundwork for sexual kino. So I'd recommend going that route since this girl may be a tough nut to crack due to being shy and conservative.

I gave several examples of types of kino moves you could do, but you have to be creative. The key it to provide a reason for touching her so you don't seem like you are manhandling her for no reason. The same way that you tell girls the reason you approached them, you should also do the same when touching them. Obviously, in the context of you "retaliating" against something they said, you don't need to actually say "I'm going to body slam you because you called me retarded!" You simply pick them up and pretend like you are going to throw them on the ground because you are mad at something they just said.

And its winter now, so you could grab her arms or hands and ask her why they are so cold. Learn a martial art move on youtube, like a wristlock or something. And show it to her or teach her to do it on you. Then every once in a while you can be like "Wu-aw!" and strike a martial art pose to prompt her to fight you. Then you've got things like palm reading, the trust test, even goofy little hand games like thumb war. Tell her you are the undisputed intercontinental champion of thumb wars and pretend to try really had to beat her, but let her win. Then pretend to get all pissed off at her and tell her she cheated and then grab her and do that body slam thing I told you about.

Starting to get the picture?