I've not taken my bike on a flight in years (2008). Back then, I rode it to Heathrow, turned the handlebars sideways, and handed it over to someone for my BA flight to Germany. (A year later, I came back by train as it was easier and I wanted a few days cycling around Paris on the way back.)

No box, no bag, nothing. They then wheeled it to wherever it needed to go. Arrived fine. Nowadays, I just hire one the other end, as I'm too lazy to buy a case and prep the bike both sides of the journey, but I'm starting to re-evaluate that as I want to do another bike tour at some point in the near future.