#1 choice - Bring the bicycle in to the room with you. Then if you have to, undo the handlebars and twist them.
http://img-3.gizmag.com/flipphandle.jpg ... 2070045668
That would not take up much room at all inside your motel room, and its easy to do. Any average motel room in North America has plenty of room.
#2/3 choice - Inside the vehicle
#2/3 choice - motel storage room, locked to something inside the room. Most motels would have that.