You definitely must have a really high cadence to experience any bouncing on a sprung Brooks. I have a champion flyer special and got it when I weighed 330, I am at about 300 now and I love it. You really don't notice the springs being there from normal riding, but they help to soak up a lot of the bigger bumps.
If I get my cadence up really high I do get a little bit of a bounce, though I get the same sensation on any saddle when my cadence gets too fast.