|MadSci Network: Physics|
"A body in motion tends to stay in motion, and a body at rest tends to remain at rest." This is called inertia. In order to change the state of motion of a body, it is necessary to push or pull on it.
When the bus starts, your body tends to remain at rest, which makes you fall backwards. The seat must push on you so that you will follow along with the motion. When the bus stops, your body tends to keep moving, which makes you fall forwards.
Try the links in the MadSci Library for more information on Physics.