I think it can be done. You're not going to lose any significant muscle mass because of riding, as long as you don't exercise to the point of exhausting your glycogen stores. One hour isn't going to do it. You might start seeing your body break down the muscle if you go 3+ hours without any on-the-bike sustenance, or if you schedule intensive workouts on consecutive days without taking proper care of your nutrition in between.

That's as far as upper body muscles are concerned. I believe the jury is still out on whether you can gain lower-body muscle mass or strength while engaging in endurance exercise (working out the same muscles).

A good way to limit muscle loss is to take protein supplements after each ride. My standard routine is to drink a big glass of juice, mixed with a scoop (30 g) of protein powder, after each workout lasting 1 hour or longer.