I took my Bixler with me on a three week trip through Indonesia.
I'd built the plane with an eye towards transport, so had make it so that the horizontal stabilizer, vertical stabilizer, and wing were all detachable. This allowed the plane to fix in the original box it'd came in.
You're able to travel with LiPos on planes, but each battery should be in an individual section. I've found the packs at CommonSenseRc to be good in this regard. You should pack your batteries in your carry-on (apparently the TSA and others prefer that). You'll likely get stopped at security, but after a couple questions I was on my way.
I found that breaking down and building up the Bixler each time I wanted to fly was pretty problematic. The next time I travel, I'll get a wing from Crashtesthobby and use it. It'll be a bit more unwieldy, but a net positive I suspect.
I found that a cardboard box doesn't handle the moisture well. I've built my current travel case out of corrugated plastic. It has great rigidity, but is still quite light.
Be careful about voltages. Most modern electronics can handle the different voltages in different countries, but some can't.
And of course, don't travel with anything you can't afford to lose.