Why are more people driving? Unless you just mean because of population growth, but we've always needed to build new infrastructure to handle that, and the next 40 years won't be any different.
If anything, self-driving cars will reduce the (relative) number of cars on the road. Several reasons:
1. Since they will probably finish their journey faster than a human driver, they won't be on the road for as long.
2. Once we hit critical mass of self-driving cars, we can get rid of taxis (and Uber and all that), in favor of calling a self-driving car to come pick you up. These cars won't need to be out on the road trolling for passengers.
3. By the time we have 100% self-driving cars I guarantee you there will be multiple companies that are in the business of automatically arranging carpooling, which will mean more people per car (and therefore fewer cars).
4. We'll still have the option to use busses, or mass transit, like we do today. Self-driving cars might even make those options more appealing; take mass transit to the nearest stop, have a self-driving car take you the rest of the way (as opposed to driving the whole distance yourself).
Also, once we reach critical mass of self-driving cars, we can start exploring other infrastructure options for moving self-driving vehicles around besides surface roads. Remember crazy-looking highways for self-driving cars in I, Robot? I don't think we'll end up with something that looks like that, but that's the general idea.
