I think we actually need an intermediary technology before self-driving can be accepted.
Already there is proof for this. The general public is widely accepting of "lane assist" that warns you if you are drifting over into another lane, and automatic parking that is accepted (less so than lane assist but still a good start).
I'd like to see widespread driver monitoring AI in cars. The should be able to tell where you are looking and warn you if you are looking away from the road too much (ie: looking at your phone), falling asleep, or driving erratically (fatigued or inebriated).
I think with this kind of driver assist becoming widespread, it will be easier for the general public to accept self-driving when it has matured. The intermediary tech is more immediately useful and amounts to a public support campaign.