The bus is really your best choice. Mexican buses, at least the first and deluxe class ones, are nice and comfortable, with reserved seats, A/C and videos.
There is no air service from Cancun to Belize.
While most car renters in Mexico don't permit their vehicles to be brought into Belize, a few do ... but if you're going to the Belize cayes it makes little sense to pay for a rental car when you can't take it to the islands.
Belize First www.belizefirst.com