The flight instructor reported that his student was to perform three takeoffs and three landings as part of an initial solo flight requirement toward a private pilot certificate with an airplane single engine land rating. Prior to the initial solo flight, the student pilot performed four takeoff and four landings with his flight instructor. On the approach for fourth landing the flight instructor instructed the student pilot to perform a full stop landing, and to then taxi back to the airport ramp. The student pilot completed the full stop landing and taxied the airplane to the ramp where the flight instructor provided a solo endorsement and told the student pilot to perform two or three landings at his own pace. The flight instructor then exited the airplane. The student pilot then performed two touch and go landings followed by a third landing, during which the airplane bounced to the right. The student pilot applied corrective control inputs and recovered the airplane from the bounced landing. However, during the subsequent landing rollout and as the student pilot attempted to turn onto a taxiway, the airplane departed the runway laterally and impacted a runway sign. The airplane sustained substantial damage to left wing. There was no reported preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.