I fly for a living too and have had two folding bikes for weekend layovers. It's an awesome way to pass the time and great transportation when your airline sticks you in a hotel far, far away from everything.

I presently use a Bike Friday Pocket rocket.
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http://s164.photobucket.com/albums/u11/bicycleflyer/

It is equipped with Shimano 8-speed/triple using barcons. The drop bars split in the middle for packing. The whole bike fits in a samsonite 30" suitcase to which I fitted a luggage strap. I can roll all my luggage on that samsonite and I carry my 4 jepp case on the top. I can asseble the bike, or pack it in about 10 minutes.

I am sure you have learned from years of traveling experience "Less is more". Take the same approach to your travel bike. Keep the crap to a minimum. The less you have installed, the less you have to remove, or reinstall each time you pack the bike. If you can do without a computer, do it. I use a basic forerunner 101 as my cyclocomputer. Don't bother with water bottles.. just go with a hydration pack. The size will depend on how much water you wish to carry and how much cargo space you need. I use a camelbak HAWG, it supplies all my water and cargo needs and it packs completely flat for easy packing. As for cycling shoes, do you really need to carry another pair? I prefer to use the aforementioned MKS quck release pedals. I use powergrip straps and just use my street shoes. The powergrips are as close to clip-less as I have ever used.

I can go on and on.... but I will stop here. If there is something specific you want to know, just ask.