You're correct that the trip seems, at that particular time, to have taken a man right at 3 days from Auburn AL to Columbus MS via rail (plus a boat ride along the way). Both the previously mentioned Harris and Carlisle describe the same elapsed time along the same route between these cities.

Rather than a terribly formalized postal system, there are also lots of examples in regimental letters of their being carried home by individuals (for leave, etc.). So, give or take a little, one could probably presume a similar timetable (3-5 days) between these locations for personal correspondence; that said, most of that traffic would have been westbound toward Columbus rather than homeward (to Alabama). Following that logic, it seems an eastbound letter might have to wait a bit longer to find a courier headed that direction rather than a letter from home finding a friendly pocket of one of those later arriving men from the Auburn sick camps to carry it to a recipient at Columbus.