Many, if not most, municipal transit systems were privately owned in the 19th century and the private owners of these systems had no incentive to segregate the races.The lesson: Capitalism is colour-blind; governments aren't. As Owen McShane commented, this is "the history we seldom hear."
These owners may have been racists themselves but they were in business to make a profit -- and you don't make a profit by alienating a lot of your customers. There was not enough market demand for Jim Crow seating on municipal transit to bring it about.
It was politics that segregated the races because the incentives of the political process are different from the incentives of the economic process. Both blacks and whites spent money to ride the buses but, after the disenfranchisement of black voters in the late 19th and early 20th century, only whites counted in the political process.
[UPDATE: Article link added: Rosa Parks: Pursuit of Profit vs. Racism. (Sorry to those who were looking for it earlier.)]