Hi,
I moved over with my cockatiel. I obtained the paperwork from DEFRA a few months before we moved. My vet in the States had to check him over and fill out some forms which had to accompany the shipping crate on the flight over.
Once in the UK there was a quarantine period, but it was only three months AT HOME quarantine. During those three months, my bird wasn't allowed to leave the house or
come into contact with any other birds. I arranged for a local DEFRA-approved vet to come see him when we arrived in the UK, he filled out the forms, and then returned at the end of the three month period. It was very easy and straightforward. Nothing like the hoops you have to go through for dogs and cats!
Whether or not you feel your bird can handle international plane travel in the cargo hold of a plane is another matter...especially if it is only for one year. It is incredibly incredibly stressful on them, and they cannot be sedated to make it easier. I was seriously torn about bringing my bird with me, as I know they can literally die of fright. I spent the entire flight in tears, in fact, wondering if he would live through it. But I used to travel with my bird in the car quite often, and he always took it in his stride (and this was a permanent move for me)...so I decided to take the risk.
I was told at the time that I shouldn't have any trouble bringing him back into the States if we should decide to return. But I never looked into it officially, because we aren't planning on returning. I would be interested to know if you come up with anything official on the US side.
Please let me know if you have any questions. I think I still have the forms here somewhere, and unless things have changed in the past four years, I might be able to help.