Perhaps for you it doesn't save money, but I would think it would save the average person money.

For what it's worth, I just sold my car, and my cost per mile was about $0.25. I drove a used (7 years old when purchased) reliable (honda) compact (civic) car, and put a decent amount of miles on it per year (20k). My bike is in the same range when I count only my commuting miles (so all my recreational miles are "free"), but again I ride an older Mt bike. Driving a new, high performance car (or bike) will cost more than average, and vice-versa.

Of course, my cost analysis doesn't account for the health benefits many people mentioned. Ultimately, for me it is about quality of life instead of quantity of life (though biking will likely increase both).