Here's the schedule that was in effect up until the press release...
Departs from Cancun bus terminal at 10:15 pm; from Cancun airport (not listed); from Playa del Carmen at 11:40 pm; from Tulum at 12:45 am.
Fares to BC: MX$474 from Cancun; MX$440 from Playa; MX$382 from Tulum.
The press release didn't mention if the schedule was changed for this route.
I think you have to get from the airport to the bus terminal in Cancun city to get the express bus to Belize.