If most of your tours will be stateside, it's far easier to just ship your bike. Then you don't have to deal with dragging a big box through the airport.

I've used bikeflights.com a few times to arrange shipping via FedEx. Last time I paid about $50 to ship the bike. Much cheaper than the airlines.

But I also have a bike with couplers. It takes some work to pack it all in and to reassemble. Truthfully, I'm not sure it's worth the expense.