Should the bike or the rider take the jolt from a bump, and how?
This is not an either-or proposition. Your bike is hitting the bumps and supporting your full weight (minus the very small proportion of weight that might be falling at that exact moment) regardless of how you stand when you hit the bumps.

The difference is whether you're going to let the additional damping effects of the down tube, seat tube, bottom bracket, cranks, and pedals absorb some of the shock before hitting your body, and whether you take that shock on your feet (which are protected by hard soles and socks and are connected to your springy ankles) or just take it right on the sit bones (which are hard and part of your skeleton). Obviously one of those is going to feel a lot worse than the other.

It's helpful to imagine an analogous system: a very light car carrying a heavy load. Our choice is whether the load is supported on a suspension system or not. If we rigidly attach the load to the frame of the car, the load isn't "taking the hit" when the car hits a bump -- rather, the shock is worsened because there's nothing to absorb some of the energy of the shock. If we suspend the load, the total weight the car is carrying remains the same (it has to), but we let the suspension system absorb some of the energy.

You and your bike are both better off if you get off the seat a bit and let your legs (and the frame, to some extent) act as a suspension system.