I know it is the third derivative specifically because a rapid _change_ in acceleration easily puts you off-balance. A change in acceleration effects a change in the forces acting on you (F=ma). When those changes happen slowly, it's easy to adapt and change your stance to neutralize those forces, thus preventing your body from accelerating relative to your frame of reference (the bus).

You can work it out from the principles of the engines (electric motor can produce their maximum torque at zero speed, combustion engines generally produce very little torque at zero speed, especially when modulated through a clutch or torque converter which you need in practice. And that's before looking at turbo-lag), but it's also something you can feel fairly viscerally: jerk is how quickly the feeling of acceleration changes. In a fast accelerating ICE car you might find yourself sinking more into the back of the seat as the car picks up speed. In an EV you basically just go from still to pressed all the way back, and then you start to pick up speed (and in fact the feeling of acceleration slackens off as the EV reaches a certain speed, though this will also happen with an ICE once they reach their peak acceleration point).

Constant acceleration as bus passenger can be fully compensated by just leaning at an angle. This is not unpleasant.

But if the jerk (or higher derivatives) are non-zero, you have to change your "lean angle" quickly to avoid getting jerked around (which is obviously much more disruptive).