Prior to traveling with your parrot it is a good idea to associate him / her with the container in which you use to travel with your bird, whether it be a kennel or travel cage. Do not just shove him / her into it on the day of travel as this can cause quite a lot of stress and fear if you do not get your bird acquainted with the container in advance. Every bird you own should be acquainted in this way in the event of travel due to a need to evacuate your home like for a hurricane or other natural disaster, you can never be ready for.
Start by getting a kennel or small travel cage to contain your pet, preferably that can be secured in the vehicle by way of the seat belt or other means of securing it.
In advance take the time to associate your bird with the container by letting him / her explore it, put snacks in it and a toy to make it a positive experience that many parrots actually learn to enjoy and look forward too. The toy should be some what of a foot toy, easily picked up for play and not some large dangly thing that could cause harm or need you to untangle your bird from while traveling, think small but not so small that it can be stolen, safety Is the way to go for your bird and you. While driving you do not want to be distracted obviously if your parrot becomes tangled up. Make sure a feed cup and water cup are secure in the container. When thinking about water as it can spill and than be gone it is often wiser to place some of your parrots favorite juicy pieces of fruit in it instead of water. This way he / she will not be without moisture for travel, also either bringing some of your water from home in a container or bottled water to offer him / her if your travel a great distance and or upon reaching your destination. Bring extra food that the bird is accustom too, now is definitely not the time to introduce a new brand other than what he is use to and will read consume.
If you plan on a destination such as a hotel or other lodging it is a good idea to bring a mini vacuum and other items to clean up after your parrot. They are much like traveling with children, can make a mess and have needs that you need to be prepared for. It is a good idea to find out in advance if your destination such as a hotel does indeed allow pets.
Other considerations are the fact that you are traveling in an air-conditioned vehicle that does not insure that your pet will stay comfortable as direct sun and glare can easily come in through a window even with the window up and the airconditioner on. Just like for a baby it is a good idea to provide a nice shaded area in the vehicle for your bird. A shade screen can be purchased in advance as an item in most stores that carry things for babies and is a wise purchase indeed. As a panting parrot can not cool him / herself off like a cat or dog and even they should have these considerations when traveling with them also.
Another thing to have on hand is a birdie first aid kit that you can put together, it should consist of orange flavored Gatorade (for dehydration), Neosporin Ointment (safe even if eaten), Kwik Stop (for bleeding prevention), a towel In the event you have to restrain him / her for any reason and or for comfort in a kennel), small scissors (in case he / she becomes tangled up in a thread from the towel or such), a small wire cutter is a good Idea also (just in case). You can never be to prepared and usually if you have these items readily available the trip goes smoothly, it's when you do not have them and are not prepared for mishaps that they most often happen.
Having a safe trip is of course is always preferred and it can even be fun to take your parrot for a ride as he / she can learn it is cozy and always likes to be with you anyway. Many of ours look forward to going bye bye and even know which travel cage and or kennel is theirs.
Closing thoughts: Always clean up after your parrot if you stay at a hotel as the next person with a parrot will be a lot more acceptable at a facility if you do. While on the road keep your parrot in his / her container so you are not distracted while driving. Keep it neat and safe for all!