Cessna 172RG instructor reported a landing gear collapse during landing on a training flight after a bounce. The aircraft stopped on the runway and the pilots exited the aircraft without injury.

Narrative

On Day 0 at approximately XA:00 hours at ZZZ; A student and I was conducting training for initial CFI. While doing the training we had a gear retraction on landing. We had just completed an RNAV approach into ZZZ on Runway XX; with a taxing back for a departure on Runway XX. We remained in the pattern for another landing. On the down wind we configured the aircraft for landing and the student briefed a power off 180; a beam the touch down point the 1000 foot marker he initiated his descent with 10 deg of flaps and moved the landing gear into the down position. While turning base we encountered a tail wind from the west; I believe it was 280 at 8 kts. He stated landing was assured; ran finial check list prior to landing. Once we turned finial the Aircraft was slightly right of center line and 10 kts. fast. The student put in 10 more degrees of flaps and run through GUMPS (Gas Undercarriage Mixture Props safety belts and switches) checklist and verified he was slightly fast and reduced power and put in 30 degrees of flags. When we crossed the numbers; we verified configured to land; gear indication was green; at this point we were still about 5 knots fast; 70 kts. As we entered into ground affect; he began his round out for landing and the mains touched down (firm but not hard) past the 1000 markers by around 200 feet and we gained lift and become airborne again. He flared slightly and the aircraft settled to the runway on the belly of the aircraft. Once the aircraft came to a stop we exited the aircraft; it was pointed directly down the runway 2 to 3 feet right of center line. Once we were both clear of the Aircraft we verified no fire was present secured the aircraft by turning fuel off; power off. We then called the airport to have them close the runway.