The only way to save significant money is to get rid of your car completely. Most people don't do that. Keeping a car means you still are paying for insurance, oil changes, depreciation on the car, and possibly a monthly bill for a car loan.

I'd say that a more reasonable estimate of savings by bike commuting is slightly more than the cost of the gas you would have burned in the car to go the same distance.

For the first two years of commuting, I kept meticulous records of miles ridden and every dime spent on the bike. It was depressing to see bike related cost keep increasing. New tires, chains, worn out cassette, broken bottom bracket, cheap hub failure necessitating the purchase of new wheels. If you ride your bike a lot it will cost money too. Not as much as a car, but it does cost money. I finally just quit counting. I like riding the bike, and that is my reason for commuting to work on it.