I had a bike on board when I worked for Holland America.
Let me just warn you that in the Caribbean biking is not easy. The roads are narrow, no bike lanes, and everyone will HONK at you. They do it to "warn you" they are coming (as if you didn't know) but it will happen literally hundreds of times - all day long.
It is still fun, but something to keep in mind.
Also - there are sharp rocks, glass, etc. Be sure to carry enough money for a taxi if you have a breakdown. The voice of experience here.