I've boxed up my bikes and sent them across the ocean 4 times.. As to the box, they are cardboard. Just put them in re-cycling.. They are only like 5 bucks. that's if you can't find one for free at the bike shop....
.. Every trip I've had , bikes were free as long as you don't exceed your allowed weight.. Just pack it well. Get a professional opinion as how to pack the bike, if you've never done it before..
. What I don't like about putting your bike on a plane. Not sure they will honor the full cost of your bike should they damage or loose it.. So, I did take my less expensive road bike. That is probably a wise plan..
Once, I did have a problem. The bike was not unloaded in LA.. So it spent a week in Tahiti.. But, it found it's way home a week later.