You beat me to posting this. I think we'll see automated public transport using minivans that can quickly navigate smaller streets. The route home might be different each time, but you'll always get an indication of ETA. Part of the hassle of catching a bus is the last mile and the wait. If a vehicle is arriving shortly after you hail it (or prebook it) and right at your location, those two factors are eliminated.

For the privacy factor, I think people will just get used to it as they have with current public transport, or tiers will be in operation (as you suggested) or someone will inevitably design a pod-based vehicle with seats facing port and starboard and a clever door system.

I do wonder if people will be uncomfortable with other passengers knowing exactly where they live and work? Perhaps designating pickup from the nearest corner would help with that, and pricing that encourages that (to save extra turns down side streets) will help too.

I wrote a bit more about all of these likely developments here for anyone else fascinated by the rise of automated vehicles: http://www.isaacforman.com.au/n/self-driving-cars/