Buses are slower than a car by some amount. A well designed express bus system isn't much slower than however, for longer distances.
Sure an actual Metro-type system, like BART in the SF Bay area, Toronto (apparently) or the various marvelous French systems that exist, these are faster than a car. But you might not have experienced the worthless, pathetic hunks of junk that Americans build and call "light rail", these can manage to be slower even than buses and more expensive and less reliable. The San Jose light rail system is a prime specimen, a "transit system" that barely manages to be faster than walking.
Of course, when I lived in San Rosa, the bus system also had an expected arrival times identical to walking - I tested this often on Google maps in off-hours. Where I live now, the bus comes twice a day so it's a further world of impractical.
Anyway, in America, it's not just that not much money gets put into public transit. it's even just that cities were created around the car. It's that the state, civic fathers, the ruling/managing group, doesn't really think public transit is necessary so much of the money that's allocated can be passed to the rulers' friends since "no one" expects public transit to work.