I'm currently dating this girl and we just had our second date. We've only kissed once. While I don't want her to think I'm moving fast, I don't want to be slow and complacent. Is there a time when I should start trying or just wait for it too happen on it's own?
Sounds like things are doing fine. For now, I would suggest that the next step is to attempt is to get to second base. As in she touch your genitals or you touch her breasts for instance. I do think inviting her back to your place would let you know if she has interest in reaching the next level.
It is showing that you have some level of interest.