The OPs theory is bogus. There is no way that I would spend as much money on bike maintenance as I would just on car insurance and registration fees. So right there I'm ahead on a bike. Also the initial cost of a car is much higher - you can buy a decent commuter bike for $500. The cheapest new cars in the USA are around $13000. If we limit the discussion to personal costs, the bike wins by a huge margin. If you look at societal costs, the bike is the ultimate grand champion: cars are harder on roads, contribute to poor health, indirectly contribute to war, contribute to air pollution (not only from tailpipes, but from refineries, oil production, and car manufacturing), and kill 40,000 people per year in the USA. One estimate I found claims that 17 million people die in traffic accidents worldwide every year.

I don't buy into a lot of the OP's assumptions either. Lots of people in Europe and Asia commute by bike without special clothes or by doing anything different than they would if they drove a car or took the bus. Most people in the USA consume enough excess calories that riding a bike would not require any extra food. The health benefits are also being downplayed. You can be sure that bike riders are much healthier inspite of breathing in more car exhaust. Extra showers are not necessary for all commuters and depends on climate and other factors.