To stop a school bus smoothly, you should:

Feathering the brake is the correct approach for stopping a school bus smoothly. This technique involves applying gentle and progressive pressure to the brake pedal, allowing for a controlled and gradual deceleration. By feathering the brake, the bus driver can minimize the discomfort felt by passengers and maintain better control of the vehicle. This method also helps avoid sudden jerks that can occur with abrupt braking, enhancing overall safety.

In the context of operating a school bus, it's crucial to ensure that students feel secure and are not subjected to unnecessary abrupt movements. This practice not only promotes comfort but also reduces the risk of injury in the event of sudden stops or collisions.

The other methods, such as braking abruptly or stomping on the brake, can lead to a harsh stop that may startle passengers and potentially cause safety hazards. Gradually releasing the throttle is also not ideal, as it does not effectively regulate braking pressure in a way that contributes to a smooth stop. Thus, feathering the brake stands out as the most appropriate technique for this situation.