We are just years away from cars that work extremely well within a defined target area, like a city, or a narrowly defined route, like trucking - so companies like Uber will be the first to self driving cars and trucks on a wide scale.
Even with trucking it's still likely a decade or more away. Even then a lot of companies will probably employ drivers vs self-driving. Just a FYI, it's also a hell of an area to get into if you want to make pushing $90k/year or more at start and get everything from healthcare insurance to an actual pension(something that a lot of places don't even have). There is such a huge demand in the US for drivers that it's insane. Especially since so much of the business is pure JiT. Hell walmart in the US in a lot of places is paying $85k+10k signing bonuses for new drivers with benefits starting in the first 45 days, that's how competitive it is. Everything from free in-truck satellite TV to safety-haul driving bonuses and mileage bonuses on top of the flat salary.
Cars though? 15 years.