It's unclear why you think the two aren't complimentary. A car near your home picks you up at your door and takes you to a bus stop. A bus comes 3 minutes later and takes you near your office. Another car meets you there and takes you to the door of your office. You had to make 2 transfers, but didn't have to wait or walk, and no single-passenger cars had to transit the congested roads to get you where you wanted to be. You had to leave at the right time to catch the bus, but you didn't have to figure out when that was or wait someplace other than your home.
For some people that still will be too much work, or they'll still be put off by the "public" part of public transit, or they'll just be insensitive to price and willing to pay more for private transportation. But a system like that would certainly make me more likely to take the bus, and I doubt I'm alone.