Before you significantly burn fat, you have to put enough demands on the body's biochemistry, and cycling is excellent. More of that bodily response below, but first note that cycling slowly (6-11 mph) burns Calories equal to roughly 1/4 of your weight in pounds per mile vs 2/3 your weight walking or running. Of course, less stress on joints, tendons, etc. usually means you can go much farther cycling and at about 3x your walking speed, so cycling has an edge in calorie burning. As you'll see, it takes less cycling time each time you ride to tell the body it better start getting into shape.
Your muscle cells contain enzymes to rapidly burn sugar or fat for energy. If you're out of shape the fat-burning enzymes decrease in concentration (the main reason people claim a "slow metabolism") and the body barely releases fatty acids into the blood stream to be used as energy. Note that studies in the 90's made famous in Covert Bailey's fitness books (like the NY Times bestseller "Smart Exercise: Burning Fat, Getting Fit") and PBS series, as well as a 2010-released Harvard Nurses study show that the rate of fat burning (as the days go by) increases ONLY if each exercise is long enough to elicit a "systemic response" from the body, which essentially says, "Ok, burning sugar isn't good enough, so I better create more fat-burning enzymes in the muscle cells and also release more fatty acids from the fat cells during and after exercise.
20 minutes of bicycling or swimming is usually enough to generate that response, but it takes 40 minutes of walking. Running takes 15 min and cross country skiing 12 minutes, but all these times, of course, vary with the runner's current fitness level, the workout intensity, and any personal unusual biological factors. In general, the more muscles used in an activity, the less time is required. Anything LESS than these times generally does little to coax the body to get into shape.
The Harvard Nurses study whose link I provided says that women who walked slowly from 1989-2005 did NOT lose weight and women who biked less than 15 min./day GAINED 4.5 lbs on average. This all fits with Bailey's research on "systemic response."
Note that if you're out of shape and exceed 80% of your recommended max. heart rate [normally 220 beats/minute - your age in years = max beats/min] you begin to burn higher percentages of sugar and less fat. The "sweet spot" for burning fat for most people is 65%-80% the recommended max. heart rate, the "aerobic" zone.
If you go under or exceed that range, you burn more sugar and less fat and, if you're out of shape, your body replaces the used-up sugar in the muscle cells with mostly bloodstream sugar, not the significant amount of bloodstream fatty-acids (converted to sugar) that fit people do.
Of course even if you exceed the 80% max. heart rate, you're pushing your body into better fitness and better future burning of fats as long as you exceed the "systemic response" time for your exercise.