Just take the bike with you and when your done the tour, decide if you want to bring the bike home. I find it worth the hassle to bring the bike home because you spend a lot of time dialling in the bike to fit your needs as a tourist. Shipping bikes on airplanes is pretty easy anyway; box, tape and your bike tools is all you need. Make sure everything is well greased (seatpost/pedals) to make disassembly easier.

And yes, you can generally load more stuff in your bike box. Just watch your weight limits.