What i did in 2015 when i needed to do exactly this was go to a supermarket and take a load of old cardboard boxes out of a pile of them inside the shop. Nothing is thrown away down there and the boxes are there for the taking. These were cornflakes boxes and the like. Buy very many rolls of parcel tape. Partly dismantled the bike, pedals off, handlebars off, derailleur off, etc. Cable tie it all together. Wrap in many rolls of Clingfilm to hold it all together. Then build a cardboard outer layer that looks like a box. Obvs the colourful side goes on the inside. Use a few thicknesses of cardboard if you want to. Use lots of parcel tape, write BICI on the outside. It looks like a box with a bike inside. I flew back to Santiago and then left all my luggage for two nights at the airport luggage store and took the bus into the centre and stayed at the Ibis. Very nice. Clean. Good food. Dry air. Quiet - ask for a room high up, away from the city noise. Took the bus to airport, picked up the bike in box and other bags, spent last bit of money on one beer, flew home. The check in staff at the airport see a cardboard container labelled BICI. That's all you need. There's no strength in the box but there never is in a cardboard box anyway. The strength is in the way you've packed the bike. You can wrap clothes around things to protect them from bumps etc but i didn't. I happily acknowledge that this idea came from Avi Cohen OTP who has done this loads of times and showed me how to do it. We bumped into each other in a small village in southern Patagonia, Chile side. He took front forks out, etc. And he actually told the woman at check-in that this box was a rucksack. (!!!)
We spent most of a day doing this, with cups of tea and lots of chat. Hope this helps. PM me if more info needed.
