Firstly, burning fat is an all-body process, not a localized one. As long as you are burning calories (and watching your intake), neither is going to be any more or any less effective than the other. Working the butt, thighs, etc does NOT reduce fat in these areas - except to the extent that it helps create a calorie deficit and reduce your OVERALL body fat.
A stationary bike has the advantage of being low-impact, which means you can build to higher intensity workouts faster. It can take a long time (several months) to adapt your leg muscles and tendons to the stresses and impact of running, so higher intensity workouts may be a slow journey.
Of course, running is very natural, and a treadmill is a good means of keeping your running conditioning up when bad weather prevents you from running outside.
Bottom line: what equipment you use doesn't matter. What matters is the intensity and duration (and thus overall calories burned). And either is going to help you reach your goals providing you do it regularly.
Of course, there is a fair bit of scientific evidence that strength training is actually more effective in fat reduction than cardio.
M@L