We have used Kango for the past year and are pleased overall. Occasionally the service hasn't been able to locate a driver (Friday afternoons seem particularly impacted) which is a pain, but we were able to reserve drivers the majority of the time that we needed them. The app allows you to block any particular drivers that your kids don't like for whatever reason. Kango has been a lifesaver to get kids from Point A to Point B without a parent needing to leave work at 3:00.
My nanny also drives for Kango. She is a former teacher and I believe she said they require background checks and fingerprinting.
She drives for them a few times per week.
We are looking for a similar service (although from Alameda). We are considering using Kango which is a service that specializes in transporting younger children. They give you the opportunity to interview drivers in advance. Alternatively, a carpool with another classmate (of course, that means you would have to drive on occasion as well).