BunnyHop Soft Landing
If you have a modern BMX then the saddle should be super low. If it is not then move it at the very bottom.

BMX bikes are very very stiff (100psi tyres, rigid cromo frame, rock solid wheels) so you need to absorb the imact with your feet and upper body. Landing with the rear wheel first (just slightly) helps trigger the feet at the exactly correct time. Another thing that helps is that when you start descending (from the bunnyhop) you extend your feet in order to give yourself enough room for absorption.

If you don't absorb with your feet then the weakest link will have to deal with the whole impact (knees, pedals, head tube of frame etc).

Keep in mind though that parts do fail. Broken pedals and bent rims is not something unexpectable in the BMX world.