The commercial certificated pilot was landing a wheel ski-equipped airplane at the conclusion of a positioning flight on a hard surface runway. The director of operations for the operator reported that the pilot bounced while landing on the right main landing gear wheel during the initial flare/touchdown. As the airplane made runway contact with both main wheels a second time, the wheels appeared to be locked, producing skid marks on the runway. The airplane nosed down, and the propeller struck the runway. The airplane fell back onto the tailwheel, which resulted in a broken tailwheel strut, and structural buckling of the aft fuselage bulkhead. The director of operations reported that the airplane did not have a mechanical malfunction, and said that the pilot may have had his feet on the brakes when the airplane touched down the second time.