I have a P900 and have noticed the same effect. It is more noticeable on the P900 because of its phenomenal zoom but it is actually present when using all my video cameras. It's actually a product of image stabilisation. I think that it is important to remember that image stabilisation mechanisms have limits and when they reach those limits, they have to make a correction in order to keep the image framed and that is what is happening when the stabilised subject suddenly jolts across the screen. Obviously, the more you are zoomed in, the more difficult it is to keep the image framed. the harder the stabilisation needs to work and the more often camera shake will cause this kind of action.
I noticed this is worse when using a tripod and trying to pan because the camera tries to keep the original framing but then reaches the point when it cannot any longer and gives up causing a jolt.
Personally, I never use image stabilisation when shooting video or when I am shooting stills on a tripod.
Thanks for your answer!
Yesterday I had the opportunity to test another P900 and I can confirm what you say, those bumps are not a malfunction from one defective camera, in fact, it seems that all P900 have this issue.
I must admit that when we're using powerful zooms the stabilizer has a hard job to do, that's undeniable, BUT, in my opinion is not a justification. As I mentioned before I have a Sony camcorder, which operating with a 3X Raynox telephoto reaches almost the same amount of zoom than the P900 does, and the camcorder does a magnificent job stabilizing the video. What I think is that the P900 is mainly a photographic camera, video recording is just a secondary feature, so the stabilizer for this feature is not the best, and of course not comparable to a video dedicated camcorder. It's a real shame.
I have tried shooting video without the stabilizer, and even on a tripod when you slightly touch the camera the vibrations are horrible, they even create inertia, a pendulum-like movement which takes 3-4 seconds to stop, these kind of vibrations generated at large zooms are completely unacceptable and destroy any scene. I have a couple of telescopes, and it's the same kind of heavy vibrations produced by the high magnification. I almost prefer the bumps generated by the stabilizer than the horrible vibrations I get without it. The only situation when I can turn off the stabilizer is when I do not have to touch the camera at all.