I've done a bunch of these calculations, just because it's fun. I'm not cycling to save money. I replaced a 53-mille round trip drive with an 8.5 mile round trip (folding) bike commute combined with round trip Amtrak train (25 minutes each way).

I figured the "Raw" cost of my bike + train is $11.88 per round trip
($9.00 Train, $1.12 food , $0.90 bike, $.86 extra clothing). Lots of assumptions in there, including extra dry cleaning & wearing out 1 extra pair of pants & 1 pair shoes per year since I bike in my work clothes.

Raw "Driving" savings is approximately $13.25 -- that is, I save about 25 cents per mile not driven (again, lots of assumptions in there including depreciation, when I get a new car, etc.

So, in theory I'm saving about a buck fifty a trip.

However, on a "real cash flow" basis, I've actually saved around $900 in two years. Most of that is because my car insurance dropped $360 / year when I switched to bike commuting, and my maintenance expenses have been less than budgeted.