Yes, you can pick the time. We have done it twice and if you leave at 6am, it only takes 2 hours and 15 minutes. They will give you a direct trip and you don't have to stop at the airport. By leaving at 6am, you get through Montego Bay just before rush hour starts. Leaving at 9am, it may take 3 hours.
We did a split trip with CSS and CN, starting with CSS and then CN. WE did not get to pick the time because another couple was coming with us from Tower Island. Since they started at Tower Island, that couple got to pick the time, and we were just told that we had no choice. I was a little nervous because they picked 1030 on a Sunday. It worked out great because it only took 2.15 hours and we did not have to get up that early to pack.