Ships get around the solar system using a propulsion system called an Epstein Drive. I just watched the following video yesterday. The narrator talks about travel times to different planets using a flip and burn technique (accelerating at a constant rate to half way point flipping direction, and decelerating at the same rate to the destination).

https://youtu.be/hz7jETrejCQ

P.S. I love the Expanse :) I'm glad it was renewed for Season 3. Best sci-fi I've seen on TV since Battlestar Galactica.