Buses from Hopkins go to Dangriga where you have to change to another bus to Belize City. Buses depart from Hopkins Monday through Saturday at 7 am and 2 pm. On Sunday, only at 2 pm.
At Dangriga, just get the next bus going to Belmopan. If you get a James Bus Line bus, the bus will go to Belmopan and then to the bus terminal in Belize City, but any other bus will terminate at Belmopan and you'll have to change to another bus to continue to BC. The Dangriga bus terminal staff can help with any questions.
Dangriga to BC is about 3.5 hours by Regular bus; a bit quicker on a James Express bus. Fare is about BZ$10.
Municipal airport is a few km from the BC bus terminal. Taxis wait in front of the bus terminal. Fare to Municipal is about BZ$6 or $7 per taxi, not per passenger.
Have you considered flying from Dangriga?