Transit needs to be competitive with cars to really see a difference. In your own example a bus somehow takes 20 minutes longer to get downtown than walking there would, which is completely ridiculous but possible with how american transit is managed.
The transit needs to be nearly as fast and convenient as cars are. The city could take some of those 6 lane roads, dedicate a bus lane, and reduce the travel time of the bus by reducing time spent in traffic and prioritizing signals at intersections for the bus.
As for zoning, it is to blame because zoning prevents density and denisty helps support transit by increasing ridership in denser areas. If every building is limited to 1 or 2 stories and has a massive parking lot, it takes more space and everything gets farther away, increasing travel times for all transportation. This also increases the costs of road maintaince, sewer and water pipes, elecitricity delivery and is just pretty much one of the most ineffecient ways for a city to use space and resources.