The pilot reported that during the first touch-and-go landing, the touchdown was firmer than normal and the airplane bounced. The pilot recovered from the bounce and continued to land. As he lowered the nose, the nose wheel collpased and the airplane veered off to the left side of the runway. Postaccident documentation of the runway identified witness marks on the runway that indicated the nosewheel strut had impacted the runway, followed by some distance later the nose gear fully collapsed, which resulted in substantial damage. The pilot reported no preimpact mechanical malfunction or failure with the gear that would have precluded normal operation.