Busses leave Playa for Chetumal many many many times each day. I dont have a schedule, but can assure you that there are many many many departures and several bus lines that service that route. There are no flights between Cancun and Belize, the closest you can get it Cancun-Chetumal. The last time I looked into it, it was $250 U.S., way more money than it was worth. That was with Aerocaribe. I'm not sure they are flying that route anymore. Anyone else reading this board haave a more recent experience flying between Cancun and Chetumal. Is it Atlantic, Mexicana, Taca, Aerocaribe or another airline company?
http://www.aerocaribe.com/ is one website you can check, but they are updating it right now.