Re: Some points
I don't see where you included the cost of your time. Let's assume that the bus is free, and the car costs (using US IRS expense rules for 2014) $0.56 per mile, and it's a 20 mile drive/ride. The car averages 30mi/hr, costs $11.20, and takes 40 minutes. The bus averages 15 mi/hr and takes 90 minutes. Both involve incidentals, like tolls and parking for the car, the time waiting for the bus, having to take the bus at a particular time, etc. The difference is 50 minutes and $11.20. So unless your take home pay is less than $14.40/hour (60/50 * $11.20) you are losing money on the bus. (The incidentals can get complicated, are subject to judgment calls and greatly depend on the particular situation, so there's no point in trying to decipher all of the possibilities.)
But I've _never_ had a situation where the time I spent on the bus wasn't more costly, even at near-minimum wage, than driving if I had a car, which I didn't. I take it back - when I went back to college (early 2000s) I lived right on a bus line that went almost straight to my school, and ran every 11 minutes. My bus pass was $45/month.
I had a job once where I had to take the bus, my job started at 2AM. The last bus I could take to town was a combined route, so I had a one mile walk to get to the nearest stop. I had to catch the bus at 12:05 AM, and it got to town quickly, about 12:25AM. I then had one and one-half hours to kill downtown before I could go to my job. I would very much have loved having a car then!
I'll just add one more tidbit. Back a couple of decades the London bus drivers went on strike. For the duration of the strike, average traffic speeds in London increased by more than 50%.