If you are taking your pet bird to the vet for their checkup or because they are sick and need to seek medical attention, you will have to do a few things to make sure that the bird is comfortable and safe when traveling.
It will depend on your bird and the size of it as to the accommodations that you have for traveling. Usually one properly sized cage or carrier will be just fine for most birds unless you have a bigger parrot. They will need to have better and bigger accommodations for travel.
You do not have to buy a carrier for your bird when they are going to the vet. Chances are that they will not have to go very often and it could just be a waste of money. You can instead use a small box or other type of carrier with a towel draped over it. This will darken up the space, which will better relax the bird. Just make sure that you leave a couple of air holes for the bird to breathe in.
Place a towel in the bottom of the box as well. This will provide the bird with secure footing so that they do not slide around in the box while the car is moving. You do not want the bird to get hurt if you would go around sudden turns. You may even want to include their perch if you can inside the box.
Place the carrier where it will not be able to move around or fall. You can put it on the top of passenger side floor or on the seat with the seat belt over it. This will secure it and keep it in place. If someone is traveling with you, it is a good idea to have them places the box between their feet and this will keep the bird safe while in any driving conditions. Avoid putting the carrier with the bird in the trunk. The exhaust fumes will kill your new pet. Also never, put them on the dashboard when you are driving. This is dangerous and they could fall off and be killed.
Never let the bird fly around the car while you are driving. They could cause interference with you while you are driving and this could lead you to a car accident or ticket. The bird may also get hurt or fly out once the doors or windows are opened up.