Car rentals

Several of the Cancun (maybe most?) allow cars to go into Belize.   For families it has been cheaper, in the past, to get the cheap airfare into Cancun on multiple passengers, then rent a car to go see Belize.
The road is not great, but passable.  You can get from Cancun into Belize in an easy day, then move around from there.
Not sure about price comparison but I think cars are cheaper per day in Mexico than they are in Belize.

The bus in Belize is not the best way to see Belize unless you have lots and lots of time and plenty of patience.   The Belize bus system is old school buses,   seats are not great. The buses are not air conditioned and they stop a lot!

If you are willing to take a little risk, you can get to Belize City without an advance reservation and then haggle with the car rental companies at the airport for a better deal.  This would work if you are in off season,  not Jan -April.   If you reserve online with Hertz, or Budget, they are only fronting for a local company.  The major car rentals do not have actual offices in Belize.   They contract with a local provider.
Be prepared that the rental cars are not like the U.S.  Cars are older, high miles,  usable but just not plush.

As you plan trips, there is a highway on the maps called Coastal Highway, also know as Manatee highway, from Belomopan to Dangriga.    This is 37 miles of unpaved road.  Can't be driven in Rainy season and the car rentals specifically forbid taking a rental on this road.   (In dry season it is a beautiful drive!)