I think the 'self-driving' feature of the car will be more like an autopilot - you'd still need a human at the wheel to occasionally override the system.
Hence, I see the self-driving car to be more of a competition to short-term rentals like Zipcar. In situations where you don't want to drive (have to work/talk on phone; after a you've had a few drinks etc), you'd still need a driver.
I think we will see self driving cars in regular use that do not require an attentive driver on the freeway within 6 years. I think self driving cars will put Uber drivers out of business in 10 to 20 years.
Even if the technology becomes publicly usable (stretching it), there are bigger obstacles - government regulation and fear mongering - that make me think it will not happen in this timeframe.
Hence, I see the self-driving car to be more of a competition to short-term rentals like Zipcar. In situations where you don't want to drive (have to work/talk on phone; after a you've had a few drinks etc), you'd still need a driver.