If you go car free, there's tremendous savings. If you're not car free, there's almost no savings.
If you still keep the car in the driveway and pay for insurance, that's the majority of the expense of having a car anyway. The rest is gas and maint and gas and maint on a reliable car is not much. Gas is about 10 cents per mile on my Toyota Corolla (30 mpg, $2.80 per gallon). Maintenance is only 5 cents a mile maximum.
My commute is 15 miles round trip. At a savings of $0.15 per mile if I commute 250 days a year, which is almost everyday, I only save $562.50. That's not that much. If you buy a beater bike, you save money. If you buy a decent new bike, you lose money.
If I could get rid of the car and sell it, I would save money. As it is, I'm losing money.