The general rules of dating a shy guy are applicable to dating a shy girl as well, here are the things that need to be taken care of if your lady love is shy and you want to bring her beyond her inhibitions. When you first start seeing her and try to engage her in a conversation but get small replies, do not confuse it with being rude or arrogant unless she actually snaps at you. People who are shy are generally considered high headed, but that is not the case most of the time. Understand that this girl is a bit different from the other girls you have dated or have around as friends.
Getting to know someone who is shy can be a frustrating experience, especially if you don't know the reasons why that particular person is shy. In a dating situation you may read the signs wrong or not be able to judge if she is actually into you or interested. I've always been a shy girl myself, so below is some very good advice that I would give to people who would want to date a shy girl, as well as what has worked and what hasn't when someone was dating me. Before you even consider to date a shy girl or befriend her, it's important to understand that people are shy for their own reasons. Some girls are shy because they have had a bad experience in the past, such as getting bullied for being the "know-it-all" in class while others learned from their parents to never talk unless spoken to. Some girls are also more shy around boys, especially if they've never had someone interested in them before.
Just because she's shy doesn't mean she's not confident. Please don't mistake being shy for not being self-assured. She's confident in who she is and knows what she wants, even if she may not always appear that way. She's independent. She's perfectly content on her own, thxvm.
It is simply a personality trait. First, try getting to know her. Then, work up the courage to ask her out.