Im sure you could bring the bike,but dont think you could ride it on the ship! ..but a good idea for the ports! I know bikes break down to nothing,so Im sure it would be ok,but you can always ask them!
I would definitely call Celebrity and ask. My concern would be keeping the bike in the cabin, there is not usually alot of extra space. Maybe, they would be able to store the bikes for you. Have a great trip.
I think that's a great idea too, I would love to bring bikes to the islands. I'm sure it can be done, you won't believe what I saw being driven off an RCCL ship in the caribbean...choppers, big, loud, obnoxious motorcycles tearing up beautiful St. Martin!
I read about this in the NY Times recently, RCL is offering theme cruises and they had a motorcycle group cruise. All the bikers brought aboard their Harley's, stored them in the hold and rode them off on the islands, and I can't believe I actually saw it. I can't remember which ship but it was this past April. Great. ;(
If they can fit those choppers onboard than surely they can bring aboard a few bicycles.