You might have to contact the cruise lines individually, and multiple times (sometimes different CSRs may give different answers).
My gut says no. You would have to check the bike like on an airline. The bike would have to be placed in the hold by the porters then brought to your cabin. At each port you would have to pass through a metal detector with the bike.
Here are Carnival's
You might be better off investigating local bike rentals at your desired ports of embarkation. Also realize that some islands do not have the best of roads and some "exciting" drivers. And, hey, maybe you would enjoy a different type of adventure for a while.