Folding bike for world travel - not touring
 

I am looking to travel for the next 2-3+ years and will only be taking a small backpack.

I would like to also bring a folding bicycle. I only want to keep my backpack, no panniers etc.

The bike would mostly be used for riding around medium and large sized cities. Maybe some limited touring as well.

I plan on taking flights but a lot more public buses and some privately owned cars as well.

I am initially thinking a 16" folder for space savings and don't want to bring any other luggage to carry the bicycle in except for maybe my first International flight out of the USA.

Is this even possible?

I'm assuming I won't be able bring it with me on a lot of planes and buses. Can you really trust them putting a $1,000 bicycle underneath and out of my sight and hoping it will be there when I arrive at my destination 1-10 hours later?

Any ideas or thoughts?