You can catch a Novelo's or Northern Transport bus (both owned by Novelo's -- they have bought out Batty & Venus) on the Northern Highway at the entrance to the international airport. Just walk (about a mile) out to the highway, or you may be able to get a taxi to take you though when the flights come in taxis prefer to take passengers into Belize City, and get on just about any bus going north. It's 2 1/2 hours or so to Corozal Town. The bus goes through the main part of Corozal Town and will drop you off or you can go on to the bus station toward the north end of town.
Consider renting a car for the Corozal part of your trip, as it's handy to have on in Corozal -- you can explore a lot of interesting areas that otherwise you would have to visit on an expensive tour.