PID values have not much to do with the "taking out the bumps" The motors can correct only angular movement, to take out the bumps:

1. Gimbal needs to be well balanced, otherwise the bumps will cause added imbalance and possibly angular movement.

2. the gimbal needs to be solid. Otherwise the bumps will cause the gimbal flex and it needs to correct angular move movements.

The bumps are not noticeable in long distance (when it is only up and down movement) See this video and compare the fence and the boat further away:



Do a horizon test like on the above video. If horizon stays on the same place when walking, then there is no angular movements due bumps.

Do a simple test, but your finger in front of you and close one eye at time. Notice how much your finger appears to move compared to background. The same happens when there is an object near the camera and the camera moves up/down or sideways. If also the object near the camera is moving, then this movement is not so visible.

3. The best way really to filter bumps out is not to bump.

Yes, as mentioned, balance and tuning are important, and no flex on gimbal or bumps will cause angular movement and that shows also on horizon.

The above video was normal walking, so sharp hits when feet hits the deck and plenty of up and down movement as seen from the fence.

If you look the 2 buildings at the middle of image and mask the rest of the video with hand etc. there is not much movement on those buildings. There is some yaw movement, but that is because of too sharply reacting follow yaw. i.e the follow yaw could have been better tuned and for this video it would had been better not to use follow mode at all.

My understanding is

Stability: less prone for vibrations, keeps well its positions even in fast moves, smoother operation with the cost of the precision

Presission: Angular error is small. Often makes the gimbal probe for vibrations etc.

I suggest tuning first for stability and then moving towards precision if needed and if the gimbal can take it.