Re:
Have a search on line, you can hire boxes.
Bags are OK for local transport, but if you are going to trust you bike to baggage handlers, you want as much protection as possible.
The first time my son took his road bike to Portugal, we put heavyweight cardboard in a borrowed bag. It worked, but the whole thing ended up weighing a ton. The next time he went he hired a hard case for a week, and was able to pack all his nutritional powders, bottles and other stuff in the case, and was still under the weight limit.