I just watched Bruce Lee: Warrior's Journey the other night. In it showed an old film clip of two opponents (one of them with an arrow saying Bruce Lee) fighting in full sparring gear. The narration said it was one of Lee's first and very few matches filmed (as a demo for full contact sparring). The film was black and white, somewhat grainy so presumably this is what you're talking about? They didn't name the other opponent.
But I understand that Lee did demos for Ed Parker's tournaments as well. Unless they are the ones where he's in a suit (jacket, turtle neck and slacks) talking to the audience and giving his famous 1 inch punch demo along with one finger push-ups.
You might see if your Blockbuster or Hollywood video has it in stock or see if it's on a NetFlix movie listing.
It's a worthy documentary either way and shows the full pagoda fight sequence of Game of Death (sans the rest of the crap they tacked on after his death). It is also interesting that you hear Lee shouting out in his native Cantonese in the film at the end and speaking english in his own voice without that stupid tough guy voice dubbing they did for his other films.