I do not use any box for my bike. I ride to the airport, dismount, roll my bike up to the ticket counter and check it in. Most times it is no problem. All airlines except Southwest will take your bike this way. I do not remove my panniers, as they provide protection. I do normally remove the pedals and put them in a pannier. I also remove the pump, water bottles and handle bar bag. Some airlines will give a large plastic bag to protect the other luggage.
The bike is handled with more care and is hand delivered at the destination. I know it sounds like it could be damaging to the bike, but watch the bike boxes as they come off the luggage systems and see how many are damaged.
This also has the added advantage of no disassemble or reassemble.
I have toured in 35 countries and flown many,many, many times, this system works very well. As with anything when traveling, give yourself plenty of time, smile and be pleasant. Most ticket agents have not had a bike travel this way so it takes a little convincing.
If you must box your bike the airlines will provide a box. You must notify them in advance and sometimes there is a charge. These boxes are avalible at almost all, world wide airports. Check with your carrier when you make your reservations and when you reconfirm on return.
Have a great trip. There is no travel like bicycle touring.