I'm military (AF), and I shipped a bike from Aviano, Italy to Florida a few years back, and the chowderheads that moved it just put it on its kickstand in the crate and called it good. I had a ton of damage when I received it.
The AF has changed the way they move things now. As long as you don't break your total moving allowance, you should be able to find your own carrier and get reimbursed. You can ship the bike separate from your household goods, but you have to have that agreed to before you ship it. Find a company that specializes in bikes. Here on the continent we have a lot more options, because everything goes by truck.
The main point is, shop around, find a good carrier, and talk to your traffic management folks and see what they can do for you. Sorry I couldn't suggest a carrier. I would have just gone to google and looked, but you can do that. FYI, the company that jacked my bike up was called Covan. It was their Italian counterparts, but even so, I won't use them again. Good luck!