The car was traveling northbound on the Richmond Parkway near West Gertrude Avenue around 12:45 p.m. when the driver lost control of the car.
The car crossed the center divide and collided with the bus.
The speed limit on Richmond Parkway is 50 mph, but police believe the car was going much faster at the time of the crash.
The car became stuck under the front wheel of the bus and was dragged almost 100 feet before both vehicles came to a stop.
The two people in the car were killed. The driver of the bus was uninjured.
It took four hours for authorities to pull the bus off the car so the remains of the victims could be removed. The victims' identities have not been released.
The bus is owned by Richmond-based First Student and was on its way to Santa Rosa for a pick-up.
