Newton’s first law states that, without any external force, if a body is at rest, it will remain at rest and if the body is moving with constant velocity, it will continue to do so.
When the moving bus decelerates, due to inertia, the body will tend to move in the forward direction of the bus. Therefore, you fall forward when the moving bus decelerates to a stop. Again, when the bus accelerates from rest, due to inertia, the body will tend to maintain the rest position. That is why; you fall backward when the bus accelerates from rest.
The tendency of a body to remain at rest or in uniform linear motion is called inertia. The reference frame to which it applies is called inertial frames. When the train is starting or stopping, there is no net force acting on the observer. So the observer is in the inertial frame. That is why; it is easy to face the side of the car because both the frame (one is observer in the car and the other one is the outside of the car) are in rest. But when the car is running at constant speed, the observer in the car does not remain at rest. The frame is not an inertial frame. That is why; it is easy to face the front or rear when the car is running at constant speed because the car is in the forward direction.