I've never moved with a bird but we did bring him home from two hours away. I got a carrier from petco and he really seems to have no problem with it. I added a better perch than the one it came with so he would have options. I also put spray millet in there for a snack, and like everyone else said you can put watery fruit to prevent dehydration. We take him on short trips with the carrier buckled up in the car so he gets used to it. This worked with my cats and I figured it would work for a bird too. We go to petco and let him pick out a toy or we take daddy a sonic drink at work some Mondays while I'm off work. He particularly likes getting out and riding on my shoulder. I just put a handd towel on my shoulder to catch any poopies.
When I first got my cats Bryan and I were dating and living in the same apartment complex, but not in the same building. So every night when I got ready to head over to his place for T.V. time, I didn't have cable, I would load them up in the carrier and take them to his place, where they got all kinds of attention and had a whole set up. Litter box, food bowls, toys and a bed. So they assocaited going in the car with good things, because EVERY day it led to wonderful and OCCASSIONALLY it led to the vet.
So in short, no matter how long you have to travel or what kind of carrier you use, work on helping your bird associate the carrier and car rides with good things. A lot less stressful than putting a ticked off animal in a car with you for a trip or a move.
http://www.petco.com/product/9601/PETCO-Bi...at=OnSiteSearchThis is the bird carrier I have. He can see out the sides and the top and you can attach small screw on perches and toys in the slots like you would the bars of a cage. It is plastic, so it COULD be chewed up, but if you put a few little toys to occupy their time in there it usually doesn't get chewed.