The first time I flew to Europe with my bike, I used a cardboard box, and left it propped against a dumpster at Gatwick Airport and pedalled away. Luckily nobody thought it was a bomb. I bought a new bike box at Gatwick Airport for the return journey, but that's getting harder to do.

since then I have just put the bike on the plane unboxed and unbagged, just took the pedals off, turned the handlebars sideways and lowered the saddle. This works best if the bike is obviously a tourer with front and rear racks and fenders, most people realize that a bike like that would be more difficult to box up. One time British Airways gave me a big transparent bag to put the bike in, but that's the most I've had to do.I've used this approach with Aer Lingus, Lufthansa and British Airways with no problem.

The longer your tour, the greater your chances that the cost of storing any bike container is going to be greater than the cost of tossing it and buying a new one for the trip home, unless you have friends/relatives who can store it for you. If you book a room at the same hotel for your arrival and departure They might be willing to store a bike box (or other luggage) for the duration of your tour, but again the odds of doing this will go down with the length of your tour. Some airports, hotels and hostels have luggage storage facilities, but again there will come a point where the cost of storage exceeds the cost of the bike box.