The student pilot was on his fourth solo flight and was landing on grass Runway 06 at Bagby Airfield. The approach and initial touchdown appeared normal but, as the aircraft rolled out, an undulation in the runway caused it to bounce about six inches into the air. The student applied forward stick and the aircraft touched down on the nosewheel first before bouncing back into the air. The instructor who was observing the flight from the ground, radioed to the student to apply aft stick, but the student pushed the stick forward again and the aircraft landed heavily on the nosewheel. The nose gear collapsed and the propeller contacted the ground. The aircraft came to a stop shortly after and the student, who was wearing a full harness, vacated the aircraft uninjured.