Also be aware that there are 2 bus terminals in Playa.
If you get the ADO Riviera shuttle bus from the airport to Playa, you will arrive at a bus terminal on 5th Ave (near the beach).
When you go to Chetumal, you depart from the other terminal (called Alterna). On my BelizeBus site, there is a link to a map of Playa showing the locations of the 2 terminals. The bus ticket can be purchased from either terminal -- I'd suggest the 5th Ave terminal because the staff speak better English.
I would recommend that you buy your ticket the day before you travel -- first, just to reserve a place, and second, to choose your seat -- I prefer being near the front passenger side (not the driver's side) for the view out the front & side windows.