I know everyone thinks this is a bus, but as a regular bus commuter in the bay area, I think there is room to expand here that a bus can't always meet. A few problems:

  * Bus stops are often far from homes and offices
  * There’s rarely parking near stops so you can't drive to it
  * Routes are fixed and rarely change. 
  * The process for petitioning for a new stop is painfully slow and done based on rough approximation of demand, community input, budgeting, and other red tape. I can't even guess what data they use to decide.
  * Many people can’t or won’t walk long distances to reach it.
  * The websites, maps, and schedules for buses are often very bad and hard to interpret

I can see someone like Uber filling a gap here with a shuttle service (not low density cars or SUVs).

  * They have hundreds of thousands of users in a metro area.
  * Get those users to enter where they live, where they need to go, and roughly at what time.
  * They find a group ~30 people with similar locations, routes, destinations, and times to create a route
  * It doesn't have to be door to door. Just an acceptable walking distance at both ends.
  * Dedicated stops don't have to be approved and built. Just pull over on a major street.
  * It is extremely easy to use Uber

No idea if this can be made economical of course. It also sounds like a really hard problem to solve.