Making public transportation free would reduce demand for oil/gas in cities and would lower prices people in rural areas would pay relative to it not being free.
Of course, this assumes that public transportation is only available in cities, but that's not true at all. Many European countries have extremely effective rural public transportation.
Oil is a global commodity so local demand reduce won't help much. Even if rural public transportation is good, I don't think rural people don't need a car, so they would complain about unbalanced grant.
The costs are negligible to every corp bailouts in the last 50 years or the cumex scandal. With the money corps extracted through illegal means with cumex we would have free transportation for the next 30 years.
Roads are vastly more expensive than transit per trip. If having the busses and trains full avoids yet another widening then taxes go down, and the rural + urban areas stop subsidizing the suburbs.
You need 20 or so lanes of freeway and 200m^2 of parking per car (paid for collectively through enforced parking minimums) and on/off ramps and arterials and collectors and double the per area infrastructure (sewers, water, power, drainage) to match the capacity of a single two way train line with right of way. Once you have that you need to pay upkeep on all of it which is more than the transit costs. Then you still need to widen it because it's full so you're out even more. And that's not counting all the externalities which absolutely dwarf those costs.
The 'one time cost' is something you're signing up to do every year at ever increasing cost until you go bankrupt or give up and build transit.
I don't think it only benefits city-dwellers. Sure, on the countryside the service is much worse, but on the other hand, the money spent per person might even be higher in the countryside.
Of course, this assumes that public transportation is only available in cities, but that's not true at all. Many European countries have extremely effective rural public transportation.