Basically, I have an excuse to meet up with this girl, and as much alone time as needed with her to take things forward, but I don't know how to go about it. Here's some more detail:

I've been meeting up with this girl on a regular basis for about two weeks. Not in a dating kind of way. I met her on a musician's website because we both played guitar and wanted someone else to play with.
So that's officially why we meet up, but when we do, we also chat a lot. We both connect pretty well and have a lot in common. We're both pretty shy, quiet people, so occasionally it gets a bit awkward, but it seems like there is some connection there.
This sort of thing has happened before, where it seems like I'm in the position to start dating a girl, but can't show her I like her. I just don't know what to do next.

Some tips/advice would be much appreciated. Thanks.