I saw this in A/C. The author suggests two bike boxes. Wheels go in one with 5 gallon bucket lids to cover the wheels and help keep them in place. When asked what is in the boxes, he answered bike parts and was not charged. He hauls them around on one of these little wheeled carts, bungied on. I haven't tried it myself. When I have had to fly ( and I much prefer Amtrak if it is available), I just followed the directions I found on the internet. It worked just fine. I do get a little tight jawed about having to pay a bunch of money to put a box on an airplane when ski equipment, golf clubs, tackle boxes and dead fish fly for free.
Also, in the tips section, carry the machine screws that attach your clips to your shoes (or better - sandals). If you have an asian store nearby, get something that is called "moo-he", for insect bites and stings as well as other skin irritations. Small tube, great relief.