First of all, I’ve never driven a bus. I have, however, driven plenty of cars and have had the opportunity to observe that cars differ in how easy they are to smoothly halt and accelerate. But I’ve always been able to learn and adjust, with the aim of making the ride reasonably smooth. In my estimation, though there are likely differences between different buses, there is also between-driver variation in jerkiness of ride.
Therefore I propose the following aide to bus drivers (or those who train them). Whenever there are passengers on board, the driver should drive as if there is a little old lady standing at the front of the bus and trying to hold on before the bus gets to her stop. That means minimizing jerkiness for fear of sending the little old lady flying. Most drivers should be familiar with this scenario, and it gives a tangible way to think about a smooth ride.
Ideally there would probably be accelerometers on buses, but in practice whatever keeps the little old lady reliably on her feet is probably good enough for the rest of those on board the bus as well.