I have just been to Cuba and all I can say is good luck, I did not see anything that would be even close to hiring a bike, maybe a scooter yes but as for a bigger bike no way. For starters Cuba does not import hardley a thing so you will see no Japnesse bikes, they hardly import Coca Cola because its American!!
Getting around on a motorbike would be just the shot but the whole time I was there I did not see a single, bigger bike or even like a trail bike 250 XR or nothing like that, that country is stuck in the last century, but thats why I went and liked it. Not trying to dampen your hopes but I would keep looking and look hard before going there with the expectation of finding something there, but having said that it may be possible you never know