I've never been able to sit all the way through 300 and I haven't seen Rome in a while (and the second season does not stick in my memory as well, since it's pretty silly), so I don't know exactly what you're talking about, but it sounds to me like you're describing litters and sedan-chairs. Both were known in antiquity and were particularly common within the city of Rome, where wheeled vehicles were prohibited in the day (following Caesar, though they were uncommon throughout the Republic--the city was far too crowded and the streets too narrow). How litters were managed over long distances is a question that cannot be answered, as they were not used for long distances--within the city the litter served as an alternative to wheeled transport that was faster than walking and more comfortable for those who could afford it. Outside of the city there was no prohibition on wheeled vehicles, and in any case most travel was done by sea, which was both faster and cheaper than travel by land