Hi there, we had exactly the same problem, for a hotel review website. (otelsikayet.com)
It took Google to start showing the starts and number of comments 8 months. I am not sure if there is a way to accelerate this process, but we contacted a few people from Google but it did not help. Then afteer 8 months suddenly the SERPs started shoing our snippets.
I hope this helps.
