The part from Cancun airport to Chetumal is very safe and comfortable. The Mexican express buses are excellent -- reclining seats, a/c, toilets, video.
Then it goes downhill when you cross the border. The Belizean buses are used Bluebird school buses; most of them are not very comfortable, not air-conditioned, and are not well equipped to handle luggage, but they are cheap! However, there is a relatively new bus line called Premier Lines which has 3 express buses per day from Chetumal to Belize City. They have a/c.
If you scroll through the recent posts, someone else has just posted about going from Cancun to Xcalak by bus. CORRECTION: not by bus, but by rental car.
Then you can get a bus back to Chetumal, and depending on which day you arrive, you can now get a water taxi from Chetumal to San Pedro. Otherwise, you could get a bus to Corozal (then fly or water taxi) or Belize City (then water taxi).
On my BelizeBus site, I have written full details about the Cancun to Chetumal bus trip, and the water taxi information.http://belizebus.wordpress.com/