Always travel with your bird in an appropriate carrier. Your bird will feel safer and and be safer. Something could frighten your bird and he may suddenly leap and fly from his perch. Predators are also a problem for birds that are not safe in a cage. Predators include cats, dogs, and birds of prey such as hawks.
Carriers are necessary for visits to see your avian veterinarian or traveling any place else. Your bird's carrier should be clean, with a clean perch and towel inside, and ready to go in case of an emergency. this will save precious time so you will not have to prepare the carrier when your bird has an emergency.
Your bird should have its own carrier and not be forced to share a carrier with another pet. If all of your pets have to leave at once, how could they if you have only one carrier. In addition, it is necessary to disinfect it between pets.