>>1886345You don't need or want a case.
Go to a bike shop and get a cardboard box from them. They get them in all the time and throw them away. It will be free. A larger chain store will always have these boxes on hand but a smaller one you might want to call and ask them to save one for you.
They will also likely have a bin filled with packing doodads, the fork end-spacers, plastic and foam, that you could pad it out with. You'll have to take the front wheel, seatpost, and bars off but the rest of the bike can stay pretty much together.
When I ship a bike to someone I autistically wrap and pad it all and ziptie/tape everything together so nothing can move or rattle and it's all padded out but that's not really necessary for touring you can basically just put your stuff in there quickly and it will be fine. Just pay minor attention to ensuring the sharp things won't poke through the box. I think the box can usually fly with you as a piece of luggage.
Then at your destination you can just throw it all away. Take a knife and cut/flatten the cardboard up and it won't be much for a recycling bin. Pretty easy to talk someone into letting you use theirs if there's nothing obvious and public to use.
If you want to send it to somewhere you could send it to a bike store and give them a box of beers or something to let you assemble it there. Most bike shops will be filled with people who have toured or want to support you doing it.
