We actually have some historical record to examine in this area, though you have to look pretty far back in US history to find a time when the government wasn't directly involved in the transit business.
James J. Hill built the Great Northern railroad in the late 1800's without taking any subsidies. He competed directly with subsidized railroads in the mid- and far west, consistently delivering lower prices and superior service to his customers.
As for highways, thousands of miles were created by private for-profit companies during the first half of the 19th century before highways and railways began to be taken over by government beginning with the Lincoln administration.