I've never done the analysis of whether or not I'm saving money by commuting on a bicycle. I doubt that I am. I don't really commute by bike for that reason. I mostly commute by bicycle because I enjoy it. I have an excellent route that is 90 percent on a beautiful MUP that seems sparsely used.
I do know one thing... each of my bicycles is worth more than my vehicle (I don't drive a nice vehicle, but I do have fairly nice bicycles.)
If I were ever to do the cost analysis, I think I would find that my food costs to fuel my ride are still more expensive than the fuel costs for my vehicle. I know we all complain about gas prices, but going to the grocery store is just as outrageous.