Would "the market" then work to effectively stop such discrimination, making government intervention unnecessary? In the social context of the American South in the 1950's, it's hard to see how. The majority clearly favored and benefitted from such discrimination, and, besides being the numeric majority, this group had more disposable income per capita than the oppressed minority, giving them even greater clout in the market than they would have from their numbers alone.
A bus line that required blacks to surrender seats to whites would get a much larger share of the white market than one that did not, given prevailing attitudes. It would lose much of the black market, of course, but its non-discriminatory competitor would be limited to that less lucrative market. Even if such a competitor could remain in business, which is doubtful, it could not run as many lines, nor be as frequent, which, of course, also makes it less competitive. In fact, the discriminatory bus line could well be better off banning blacks entirely. It's not going to get much of their business anyway, and the whites would probably prefer not to see them at all (if the whites enjoy the power that comes from forcing others to vacate, this might not be true. I don't understand the underlying psychology of the time and place well enough to make this call. But "whites only" seems to be what the South went for when it could, so I think it reasonable to assume that would be their "consumer preference") The logical result would be two bus lines, one for whites and one for blacks, the latter clearly inferior in service, assuming it was economically viable at all. If not, the result would be that only whites could ride busses.
Notice that this is actually worse for blacks than what racist government intervention produced. In a sense, the market here is behaving as advertised: it is filling consumer preferences more effectively and efficiently than the government does, and possibly than the government could. It is not producing greater efficiency in use of resources; multiple bus lines serving similar routes is less efficient than having one bus line. (in fact, the logical market outcome would be racially segregated bus lines run by the same company, but even that is less efficient). But that productive efficiency loss is compensated for the fact that a white consumer preference is being met that otherwise would not. The market would have to pass on this cost with somewhat higher prices or reduced service, but prejudice seems to be more emotionally compelling than minor increases in bus fare, and the public would never be exposed to the alternative to form a basis for comparisons anyway.
When the government imposes discrimination, it is imposing a social norm. When it prohibits such, it is also imposing a social norm. Although I believe greatly in individual freedom, I don't think there is any way around the fact that the government is going to impose some norms. To arbitrate which norms should be imposed, you have to get down to the substance of the norm. It cannot be a purely procedural debate.