There are many different wheeled vehicles that potentially traverse hotels on a daily basis. Examples: wheelchairs, strollers, and electronic convenience vehicles (ECVs). I don't see how a bike is much different. It's better actually, as most bikes are light enough to pick up and carry through public areas.

Of course, it's up to each individual hotel (or even each individual hotel employee) as to whether they allow bikes. If you want to be diligent, you could contact the hotel in advance.