lucille, Thor, my experience was probably a good one because I gate checked the bike. That is, I wheeled it through the security checkpoint, all the way up to the boarding gate, and gave it to the flight attendants to be hand-checked. This is what musicians do with their instruments, and the packages receive much more delicate treatment.
Also the Brompton is an incredibly sturdy bike; people don't give it enough credit for this. I would never treat it this way, but I'm certain I could ride away from a couple six-foot drops directly onto concrete. I did use a strap to make sure it wouldn't fall open, and if I were vain about the saddle or if it were made from a more delicate material than thick cowhide I'd probably put a cover on it, or remove it and add it to my baggage.
Caribbean, Europe, Vancouver... there are a lot of places I want to fly to now. It'll be awhile before I can make the time and resources line up, but the world feels wide open!