I've gone out with this girl a few times, she seems nice, but really shy.

The problem is I don't really know if she is interested in me. She hasn't done a lot to show interest, but hasn't done anything the show disinterest.

-When I make eye contact for more than a few seconds she can't hold it a looks away
-When I put my arm around her of hold her hand she doesn't lean in/squeeze my hand but she seems quite comfortable with me touching her
-Whenever I suggest we go out she says say straight away, And she will always do what i suggest where and when.
-She keeps asking me a lot of basic questions about myself but seems reluctant to get into a deeper conversation.
-I always have to lead to conversation and she will very rarely bring up a new subject or fill in the silences, but she always seems interested in what I'm saying

What do you guys think?

Yea I've had this with a girl as well, It was up to me to lead the conversations she wouldn't start it, but she was always interested in what I said and she also made eye contact several times. I think what you could do is take her somewhere she is really comfortable so she can open up, or maybe hang out with her and her friends, shes more likely to open up then. Do things that she's confident in any hobby or activity.