The best way I have found to burn fat is with the treadmill. Walk at 4 mph (6 km/h) with a 15% incline for one hour, three times a week. You will burn about 1,000 calories per hour.
You need to work your way up to that speed and that incline. Start at 3.5 mph with a 6% incline and keep an eye on your hart rate. Every minute or so increase the speed and the incline, if your hart rate goes too high, reduce the speed and keep the incline. When it comes down, you go up again.
The stationaly bike will not help much with the core muscles, but the road bike does engage the core as well as the arms and of course the thighs. It will not build thigh muscles unless you go sprinting.