Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?
In the situation of a moving bus, the passengers are also in motion along with the bus. Now when brakes are applied the bus comes to rest but due to the inertia of passengers they still tend to move in the forward direction, Thus they move in forward direction after applying brakes.
Now when the bus is rest, the passengers are also at rest. The inertia tend them to be at rest. That's why when bus accelerates they move in a backward direction.