Hotel gyms, fitness clubs. Do short hard workouts on exercise bikes. Then try to put in longer rides on the weekend.
Ocassionally you'll be in places you can rent bikes.
I tend to trave 4-5 days a month. If it was more, I'd consider investing in a folder, such as Bike Friday Pocket Rocket.
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You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.