A camp I was at told me to allow my knees to bounce. My current barn always says “knees on, you don’t want them bouncing” but doesn’t that affect the horse and what do you advise?

Both aren't quite correct. Knees shouldn't be bouncing, however they are part of the spring system in your leg (along with your ankle), and so should not be fixed. In the same way as you don't want your car suspension bouncing around, you don't want your knees to bounce. Keeping your weight in your toes should keep them strong but supple.

Any movement of your movement should be done with the horse's movement. Riders that look completely still are actually doing a huge amount of moving. They're just moving with the horse, rather than moving themselves or trying to keep themselves still. Again, to use a car analogy, but if the car's suspension is too stiff (i.e. like trying to hold your knee still), the car essentially has no suspension and will bounce going over a bump, which isn't pleasant for those inside. If the car's suspension is too loose (i.e. like allowing your knee to just bounce around), then the car will continue to bounce around the place, even after going over the bump. If the car's suspension is right (i.e. a strong but supple knee), then you won't even notice going over the bump.
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