Hi, to my knowledge, it will not be possible to do this on the bus. The only way to do it would be to find a taxi driver who is already going from Havana to Santiago and to pay him to take the bike with him. The chances of you finding an honest driver to do this for you are very small.
Bikes are very precious in Cuba. One bike is transportation for a whole family. Theft is very high. I would never let the bike out of my sight. Even people at the bus company would likely try to steal it if you tried to send it without you.
Your best option is to bring the bike with you at all times and to bring it yourself from Havana to Santiago. Also, is the bike a good bike? Like a racing bike or a special mountain bike? If the bike is good, be extra careful. If the bike is just a cheap bike to use as transportation, then consider simply renting a bike while in Santiago. It might cost you 10 to 20 cuc per day to rent a bike, but it is easier than dragging your own bike all around Cuba.
Take care,
Mario
