How many 3rd party documented fights did he have? Do we have footage of him really fighting anywhere?
If you know a way to travel back in time to the 1960's and record video footage... go right ahead..
in the meantime, you can try looking for pics or videos of the 1964 or 1967 Long Beach International Karate Championships.
In 1964 Lee performed repetitions of two-finger pushups (using the thumb and the index finger) with feet at approximately a shoulder-width apart.
In the same Long Beach event he also performed the "One inch punch", the description of which is as follows: Lee stood upright, his right foot forward with knees bent slightly, in front of a standing, stationary partner. Lee's right arm was partly extended and his right fist approximately an inch away from the partner's chest. Without retracting his right arm, Lee then forcibly delivered the punch to his partner while largely maintaining his posture, sending the partner backwards and falling into a chair said to be placed behind the partner to prevent injury, though his partner's inertia soon caused him to fall to the floor.
His volunteer was Bob Baker of Stockton, California. "I told Bruce not to do this type of demonstration again", he recalled. "When he punched me that last time, I had to stay home from work because the pain in my chest was unbearable."
In 1967 Lee performed various demonstrations, including the famous "unstoppable punch" against USKA world karate champion Vic Moore. Lee told Moore that he was going to throw a straight punch to the face, and all he had to do was to try and block it. Lee took several steps back and asked if Moore was ready, when Moore nodded in affirmation, Lee glided towards him until he was within striking range. He then threw a straight punch directly at Moore's face, and stopped before impact. In eight attempts, Moore failed to block any of the punches