Hey man,
When a girl is shy, or conservative in her attitude, dress, and company, she is what one calls a "Prude". Girls at our age all fall under two categories, "Prude" and "Purd". Now they are not usually one EXTREME or the other, they are usually a mix of the two; however, it seems as though your girl is pretty extreme Prude. Here is the very short version of how to deal with Prudes:
Be light on Negs, heavy on stories, banter, future projections, cold readings about her (such as the Cube), tongue in cheek romanticism, and NLP. The main goal is comfort, not attraction. Don't be afraid to tell a sensitive story that shows you're human and you have problems sometimes too. Also, show that you're looking for more than just a hot girl (Mystery's three important things gambit/neg is good for this). Keep in mind - kino escalation will be slower than it would be with a Purd, but that does NOT mean "don't kino." If you do not kino, you may end up in the friend zone. A few ways to avoid the friend zone are - show that you are a sexual being (do this through kino, and stories), let her catch you staring at her lips on day 5 (estimate), etc.
Hope this helps!
Happy Gaming

-Saint Pixie