The student pilot reported that he was landing on runway 27 at the conclusion of a solo cross-country flight when the airplane bounced on the main landing gear. He stated that he flared more, but the airplane bounced again. He added full engine power to execute a go-around, and the airplane rolled to the left. Application of right aileron and rudder controls to correct the roll was not effective and the airplane continued into a grass area off the left side of the runway. The left wing and propeller impacted the ground, and the engine separated from its mounts, resulting in substantial damage. The student pilot stated that there were no mechanical malfunctions or anomalies with the airplane and data retrieved from the airplane's primary flight display also revealed no anomalies. The reported wind at the airport about the time of the accident was from 340 degrees at 5 knots.