The pilot reported that during final approach, he increased airspeed from 65 to 70 mph to compensate for light windshear. Upon touchdown, the airplane bounced twice and he increased engine power slightly to allow the airplane to settle on the main landing gear. After it settled, the nosewheel collapsed substantially damaging the firewall. The airplane then came to rest upright on the runway. The pilot surmised that the second bounce must have separated the nosewheel. A witness to the accident, who was also a Federal Aviation Administration inspector, stated that the nosegear touched down first, followed by bounces with two or three more nosegear touchdowns, before the nosewheel collapsed and the airplane came to rest. The recorded wind at the airport about the time of the accident was a left crosswind at 8 knots.