It is polite to bring with you your own bed cover and use it in place of the hotel's bed cover to keep it free of dog hair.
Do not wash your dog in the hotel's bath tub or use the hotel's towels on your dog. Disposable bath wipes are available for freshening your dog between baths and are suitable to use when traveling.
Do not leave your service dog unattended in your hotel room. He may surprise housekeeping.
Take a collapsible crate with you for emergencies. A basic sport crate that will fold small enough to fit in your luggage is available for as little as $25.