I made the drive from BC to Placencia this week. It was lovely. Great scenery and a chance to stop at some nice spots along the way.
Don't miss Belize Zoo, Art Box Gift Shop (belmopan entry road) and the Inland Blue Hole.
If you are hungry the Texaco gas station near the Dangriga turnoff has good chicken tortas. You do need to plan on the family feed for the trip - after you pass Cheers, JB's and Amigos (all next to each other on Western Highway) you are fresh out of restaurants til you hit Placencia.
Rental rates for cars are a bit hig, but you can see so much more with a car - if you can swing it, I'd get one.