Why does it happen?

If a stationary bus suddenly speeds up, passengers are thrown in the backward direction.

The given situation is a case of inertia at rest. Every object would like to continue its state of rest or uniform motion until an external force is applied. Inertia is actually a measure to resist the change of state. A stationary bus would like to be stationary in the absence of any force. It is called the inertia at rest.

Passengers in a bus at rest will be also in inertia at rest. Even when the bus suddenly speeds up, the passenger’s body will be on inertia at rest to resist the change. It will results in the backward motion of passenger.