Why do you say "it doesn't really feel like more than a good friendship"? If there is ANY ambiguity on whether you guys are dating, you need to make it unambiguous.

In terms of getting closer to her, don't overthink it. Get her to talk about herself, but without making it seem like you're interrogating her. The conversations should just flow and there should be an exchange of information (i.e. she's getting to know you more as well). I generally don't bring up relationships/love before she does. For whatever reason, it generally works better if you let her bring it up first.

If you're not a good talker, plan dates where you guys are doing something. Indoor climbing, go-karting, cooking a meal together, etc.

A lot of people will tell you to break the touch barrier ASAP, but focusing on it too much comes off as super creepy. What you're looking for is some opening and reciprocation. If you're in a loud bar for example, ask her what she wants to drink by placing your hand on the small of her back or her waist and leaning in towards her ear. Her body language will let you know whether she is comfortable with the closeness and physical contact.