For travel safety, put your snake (either in a cloth bag or in the tub as described ^ IF it will fit) into an ice chest. This will protect your snake from excessive sun in your vehicle during a trip of any length & keep his temperatures stable, not to mention the fact that if you want to stay in a motel, this will merely appear to be food snacks, not snakes, that you brought with you.
Been there, & done this...motels/hotels haven't got a clue. Paid pet deposit for my (very obvious-) dog, but they had NO idea that I had a bunch of snakes with me, lol. (moved halfway across country some years ago) And having a well-insulated ice chest on hand is just never a bad investment, ok?Snakes are good travelers this way, & each night in the room, I visited with them briefly & offered water. They were just fine & mostly slept thru the trip- they felt safe.