We took a bike along to Europe on Delta as checked luggage. This wa few weeks before they officially announced no surcharges for bikes, and they already charged us nothing as it fitted our checked luggage allowance - one of us had a frequent flier bonus of an extra piece. For packing, we went to a LBS and they told us to dive into a dumpster behind the shop to find a suitable box. We picked up two and used up one for packing and the other cut up for extra padding and sealing. We went through the steps of making the bike flat and rugged and it had plenty of accessories.
As a warning, one item we took of was a rear derailleur and it turned into a problem at the other end. As we assembled the bike in front of the airport and in mounting the rear derailleur back, we mangled the thread in the hanger. All ended well, as a LBS at the other end repaired the thread at nearly no cost, but there were tense moments there, Essentially, prepare yourself psychologically for some hiccups around the bike too, as otherwise common with travel/relocation.