Not sure this a really about physics, but anyway: I only ski bumps when I need to, have found that a flex pattern of a soft tip and tail with a moderately stiff mid-ski is most effective. I want the ski to hug the terrain, help me scrub speed or change my mind in a nanosecond, and I don't want a stiff tail to load and release at the wrong moment. Softer ends also are more forgiving when you get your CoM out of whack, which can happen if you're being assertive. But a bit of stiffness under boot is good for icy downsides. If you're skiing something with tip and tail rocker - highly recommended for bumps - then you can get away with a bit more stiffness overall. I regard skis like the Bushwacker, TheOne, and the BMX88/98 as ideal for bumps in the trees, and many of the freestyle group (THall, Extreme, Rotor 84, Dead Money, for instance) as ideal solutions for slope bumps. IMO, wood is king, carbon can be a good thing, metal not so much.
Finally, less weight and less sidecut will help with pivoting and smearing quickly. Some folks claim to carve bumps, but I don't much unless they're very large and very icy, and I don't see a lot of it on the mountain, unless you're talking about take-no-prisoners mogul flattening with a fat heavy GS. Which may work on a short stretch of softer bumps, but will get you up close and personal with a tree if you're in the woods, and is best reserved for folks with relatives who are orthopedic surgeons.