If there's any way you can ship the bike to yourself at your destination, then you don't have to schlep the box through the airport. It isn't necessarily any cheaper than flying with the box, but you can pack a whole bunch of other stuff in the bike box, which both helps insulate the bike, and is that much less you have to pack on your flight. Plus there's less likelihood of the box being opened by TSA agents who won't care about putting everything back the way it was.
You can ship hold for pickup at the nearest FedEx depot (I think they require a local address, but that can be a hotel or whatever), or directly to your destination.
Speed comes from what you put behind you. - Judi Ketteler