Most of the discussion here seems to be about personal cars, but there's so much more incentive to automate trucks and other commercial vehicles.
A company that buys a truck has to use it as much as humanly possible to earn its cost back and to drive it around day and night. The limiting factor is now the driver who has to eat and sleep and can't be driving during that. In Europe (don't know about US) there are very tough work and rest laws, that mandate resting every 3 hours, taking a 8-hour pause for the night etc. so that the driver wouldn't cause traffic accidents. An automated truck doesn't need rest, so it will generate twice as much revenue and less hassles - no more missing the ferry with a 3 million dollar cargo because the driver had to take his mandated rest pause.
There are rumors about some "million-truck march" or something, about the truck drivers in US going on strike? I don't really care about that but the truck-owning companies do. They will gladly replace any driver for an automated driver without hesitation.
Replacing bus drivers may be a bit more difficult... Well, not necessarily - the bus stops just have to be equipped with some kind of button to let the bus know it has to stop there and not drive by, additional monitoring for the doors will have to be added, that's it.
Both trucks and buses will probably still need some human supervision - someone to guard the vehicle and cargo, take care of the cargo documents, perhaps load/unload the cargo (currently some drivers have to do that in some ports, depending on the incoterms), in buses keep order and check on the passengers, give additional instructions to the vehicle if needed, call the police if situation should require it. But there's a big difference - the road safety no longer depends on these people to be alert and rested, so their working times are no longer bound by the existing laws for drivers. It will be more like any other current profession like security guards or hotel administrators.
I wouldn't really count on the professional driver's occupation to be around very much longer.