How does bicycling compare to other exercises when it comes to fat loss?
The main indicator of "fat burning" in different exercises boils down to your rate of calorie burn, and how long you maintain that rate.
Cycling is not a bad way to lose fat by that metric, since as you get trained up you can maintain a reasonable rate of burn for quite a long duration. Cycling burns (depending on the speed/amount of effort) several hundred calories per hour. When I'm out on a long ride I refuel at the rate of 150 or so calories per hour. Assuming that I don't completely erase that by overeating after a ride I get to keep that deficit for that day.
All this being said, cycling 20-30 minutes per day is likely to make you stronger, but not trim you down super fast.
Edit: Should have been more clear on this, but cycling doesn't burn more calories per hour than running (or some other exercises). Cycling is, however, lower impact and for some people more enjoyable than running, allowing a greater amount of time in the calorie burning zone.