Let's say for example that you actually do get a job flying internationally for someone, and let's say for example that after you've flown all night, into a 16 hour layover, in a city you probably have never been to, and let's say for example that you actually feel good enough to take a long bike ride, and let's say for example, that you somehow get lost and actually don't make it back in time for your next leg, then, let's say for example, that you'll probably only do this once, because you'll probably be out on the street the following day.
Anyway, let's say I stop being sarcastic and just answer your question. Yes, you can bring as much stuff as you can carry, but you'll need to know the type of transportation that your company will provide from airport to the hotel and back. You'd certainly hate to be on a 3 person crew and have some little taxi cab pull up, with not enough room to accommodate everyones stuff, especially your bike. Having said that, I have a classmate at FedEx who had a custom bike made for himself, that fit in a custom suitcase. He took that bike everywhere. When I was flying intra-Europe, I used to ship my mountain bike over to Milan and then ride it every day about 9 miles to the squash club, play squash for a few hours and then ride it back. I stopped after TWA trashed my bike on the way over. Luckily there was an Italian bike shop a few blocks from the Milan Hilton and they had me on my way after about a $125 bill. Took forever to retrieve the money from TWA.
You might first try using the exercise equipment in the hotel, or a local YMCA. Seriously, this international stuff really takes it out of you and I know a lot of guys who just want to sleep until supper time, go out for dinner and a few adult beverages, then back to the hotel to sleep. Or you could always go for a long distance walk in the city of your choice, but make sure you're up on where to walk and more importantly, where not to walk (or peddle, for that matter.)
Good luck.