Yes, you can take a bus from San Ignacio to Placencia, but it is a fairly longish trip, since you'll have to change buses in Belmopan and again in Dangriga. There are as I recall only two buses a day that go from Dangriga to Placencia directly, so you have to schedule your trip to make those connections.
From Placencia to Caulker you can bus back to Belize City and take a water taxi or fly, or you can fly from Placencia to municipal and fly/water taxi to Caulker, or a combination.
--Lan Sluder