The private pilot was landing on a 3,499-foot-long, asphalt runway. He reported that the airplane's final approach speed was "too fast" and upon landing, the airplane began to bounce. After the third bounce, the airplane landed hard which resulted in substantial damage to the nose landing gear and firewall. The pilot further reported he did not experience any preaccident malfunctions or failures that would have precluded normal operation, and that he should have aborted the landing after the first bounce. Winds reported at the airport, about the time of the accident, were variable at 7 knots.