I haven't toured by bike, but I have taken a bike with me on a plane or in a car, and when I have asked the hotels, they have discouraged me from bringing the bike into my room and suggested a storage room. Since I had a cheap throwaway bike, I complied, but if I had a valuable bike I would have argued. The problem with using a storage room is that you may not be able to access it without waiting for a staff person.
More recently when I travel with my folder, I just fold it and smuggle it in.
I would suggest you try to stay at a motel with a ground floor room with direct access to the parking lot, and place the bike on a tarp or newspapers, so if they do happen to see it during cleaning or room service they will see that you have taken care not to dirty or damage the room