There are no bus services on Ambergris Caye. However, on the mainland, they have a number of public buses and it's very cheap.
In order to go from Ambergris Caye to the mainland of Belize, I take a boat because the boat lands you right at the heart of Belize City in the public water taxi terminal. From the water taxi terminal, I make my way over the bus terminal (pictured) and I get on a bus to go to San Ignacio or down south to Dangriga, depending on where I want to go in the country. A three to four-hour bus ride is around US $5 but that is on a school bus; it is not a Greyhound bus. They do have the Greyhound buses in Belize. They have pretty decent express buses, but you would have to pay $10 for the same experience. It is still very affordable. The majority of the people in Belize take buses around the country because it is very accessible. I never had a problem.