Give up or keep trying with a shy girl?

Anonymous
I've been talking to this girl for about a month and she just is so quiet and nervous around me that I don't know how to interpret it. She is chatty and will initiate conversations with almost anybody she knows, greet them, joke around. She will rarely initiate contact with me unless I make an effort not to say anything, then she'll make small talk and things like that. When we talk and have a nice groove going its great, we use sarcasm, tease each other, argue playfully and can be somewhat b*tchy at times but I like it since she never shows that side to anybody else. Most of the time she is quiet around me and it drives me nuts because its only to me that sometimes I think she just doesn't like me that much, what should I do? I don't want to keep bugging her (she says I don't bug her, but I wonder sometimes) but at the same time she seems to remember every little detail of conversations we've had, that makes me think maybe she is just nervous, what should I do?
Give up or keep trying with a shy girl?
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