After a normal approach, the pilot was surprised when the aircraft bounced on initial touchdown. A second bounce occurred, during which the pilot applied power to cushion the next touchdown. The power application seemed to have little effect and the nosewheel and propeller struck the ground heavily. The aircraft then ran off the side of the runway and collided with a fence. The pilot had been given a check flight on the aircraft two days previously. During this check, he was advised to use less flap for landing than that specified in the Flight Manual. At the time of the accident, the aircraft was being operated in excess of the maximum permitted all-up-weight. The pilot advised that he had not carried out a weight and balance calculation because the hiring organisation had assured him that the aircraft could be operated with full fuel tanks and four persons on board. Following the bounced landing the pilot had not initiated a go around and directional control had been lost after the nosegear suffered damage on heavy contact with the runway.