if Mike could get off first and put hands on Bruce then he wins, but it's well documented how hard Bruce could punch (a martial arts delivered punch, not boxing, two different things form wise and etc), and kick. He could probably shatter Mikes legs, or ribs with one kick, a kick to the head and it's definitely over, same logic if Mike caught Bruce with a left hook or uppercut. Bruce should be respected just based off of the fact he was a master in a legit art, and back in his day dojo's were more ruthless than they are now, you got tested in the dojo, street, and etc.. don't be fooled by these martial arts movies, in most cases a real bare-fist martial arts street fight would only last a couple minutes tops (any street fight in general for that matter), if you ever seen two high level black belts go at it legit then you will understand...oh and Chuck Norris is just bitter/having a bruised ego in that clip..my sensei from way back is real cool with Chuck, fought him twice on some spar/competition shyt, he beat him once
Mike would win if he got close enough though, too big, quick and strong, with distance involved Bruce would probably win