we shipped two bikes to Arizona from Seattle last year via the airline.
We had my bike very very carefully packed, with nothing else in the bike box but it and a few little things. NO PROBLEMS.
We also shipped Raleighdon's old Raleigh, and put a lot of stuff in that box with it. Guess what, a derailleur got bent.
It's very expensive to ship via airlines, so you do need to shop around and see what works better.
Since bike boxes are so big, they're hard for the airlines to lose of course, although i'm sure it happens.
prices for all kinds of shipping are going up, they have to, because they're all paying for petroleum too.