Be clear about one thing first: you cannot ride to the Great Blue Hole. It lies out in the Caribbean, about seventy kilometres off the coast of Belize, in the middle of Lighthouse Reef, and the only ways to reach it are a small boat on a long day trip or a sightseeing flight from Belize City. The bike stays on the mainland, which is perfectly good riding country, and the Hole is the excursion you take once you have settled in.
What you are looking for is a perfect circle of dark blue, about three hundred metres across, surrounded by the pale turquoise of the shallow reef, which is why it stands out so strongly from the air. It is a sinkhole, a limestone cave that collapsed at the end of the last ice age, when sea levels were far lower, and then flooded as the water rose, and it plunges to something over a hundred metres. Jacques Cousteau brought his ship Calypso here in 1971 and declared it one of the top diving sites in the world, and divers still go down to the ledges to see stalactites formed when the cave was dry, and reef sharks cruising the gloom.
The Hole is part of the Belize Barrier Reef Reserve System, a World Heritage Site, and the whole region is a marine reserve, so look and do not touch. Nearby Half Moon Caye holds a colony of red-footed boobies, with a sandy beach and a lighthouse, and the water around it is clear enough for snorkelling.
For the ride, the useful base is Belize City, which has fuel and every service, or one of the coastal towns, and the Philip Goldson Highway runs inland across flat country of pine, cane fields and rivers, with speed bumps in every village and a fair amount of trucks. Belize is small, English is widely spoken and distances are short, so a loop to the Maya sites and back is easy. The dry season, from February to May, brings the calmest seas and the best visibility, while hurricanes can strike between June and November. Book the boat in advance, take sunscreen and a hat, and expect to be tired, salty and very happy.