Student pilot reported; while on a cross country flight; they bounced twice during landing. The pilot executed a go around and returned to departure airport and found the propeller was bent.

Narrative

I was flying my solo XC from ZZZ1 to ZZZ. I entered a standard left pattern at a 45 degree angle for left downwind for Runway XX when I received a clear to land from Tower. I make my final approach and I'm going a little bit too fast at around 80 knots in my Grumman traveler. I was a bit high so I decreased some of my power to descend and put in full flaps. When I landed I pitched up and must have pitched up too soon and then started to bounce; after the first bounce I thought maybe it would settle down but then it bounced again and it was worse that time. Really quickly I decided to do a go around so I put full power pitched up to takeoff and gradually took out my flaps. I told Tower that I would do a go around; because the landing wouldn't have been good. They approved and the landing that time around went very smooth. I landed and did a full stop then was given directions to taxi to Runway XX to fly back out to ZZZ1. When I flew back to ZZZ1 I landed smoothly again; cleared of runways and then taxied to the ramp when I turned the airplane off and got out I noticed my bottom propeller was slightly bent. It must have happened on the second bounce at ZZZ when I nicked the bottom of it; so I unknowingly flew it back to ZZZ1. Otherwise I wouldn't have flow it if I had noticed the damage to the propeller much sooner. I told my CFI straight away what happened. I should have decreased my airspeed on final approach and should have initiated my go around sooner preferably after the first bounce instead of the second one.