The student pilot reported that after arriving at the destination airport while on a solo cross-country flight, she elected to perform airport traffic pattern work with some touch-and-go landings. The first landing went well, and the pilot took off again for a second attempt. The second approach was stable throughout; the airspeed was good and it was smooth, but after arriving over the threshold, she reduced engine power but flared late, which did not arrest the descent in time. The airplane struck the runway and bounced. During the second bounce the airplane landed hard, and the nose landing gear collapsed resulting in substantial damage to the firewall and airframe. The pilot agreed that there were no preimpact malfunctions or failures of the airplane that precluded normal operation. The pilot further stated she just “rounded out late,” and thought it was too late to abort the landing.