There is a bus from Belize City to Chetumal on Novelos bus line departing every hour and cost is 11bz
express goes at 9, 11, 5 and 6pm cost is 14bz
Border Exit fee is 37.50BZD pay in Belize dollars or USD dollars.
once in Chet you can take a Rivera or ADO bus to Cancun...
you can see all the schedules as well as prices and even pick your seat. pay by credit card.
As for Novelos in Belize, you have to purchase ticket direct with them.
there is also a San Juan Bus or Mundo Maya Bus that departs Belize City daily between 11am and 12noon from the marine terminal for 10USD. this bus goes straight to Chet only stopping at border.