P.S. - watch/read some documentaries.
He won martial arts competitions - one very important one to establish his own school.
Sorry to pick on you Marc but you been watching too man movies

Bruce never entered any compititions as such.
He did have a fight similar to the one in the Movie of his life but it was a scrappy afair and his opponent did nothing but run away.......Bruce ended up with sore knuckles and a broken temper because he took too long to finish the guy off.
It has also been docomented that Bruce instigated the fight after the initial challenge to his teachings was withdrawn.
The reason Bruce couldn't enter competitions was it went gainst everything he believed......Shotokan Karate, Wushu or whatever, have rules...Jeet Kun Do does not play y the book if you follow my drift.
If Bruce had fought in competitions like his good friend Chuck Norris he would have been disqualified instantly. He had no interest in games of catch.
How good was he? That we will never know but he as called fast by Norris...the fastest man I ever sttod in front of by Loe Lewis (World Chamion kick boxer and student of Norris).we can take from that he was faster than 6 times world champion Norris.
How powerful was he? Norris and Lewis bought him a kick bag that was so heavy they could hardly lift it......they did it as a joke because when they kicked it it hardly moved........a wekk later Bruce was knocking the thing back so far it was almost pulling the bearings out the beam it was attached to.
The guy had amazing body strength and he could hit faster and harder than any MA of his time. There is a great story from one of his students who when he first met Bruce he told him he couldn't fight for peanuts..In his own words" The next thing I knew I was on the ground looking up at Bruce thinking what happened........Bruce decked him and the guy never even saw it coming......the guy had just left the forces (Army or namve can't remeber) where he was the undefeated heavyweight champion.
Which brings me to The MMA fighter.
Firts off Bruce was no ones fool.........he was a great thinker and all round clever guy......He would never have been as stupid to go into the ring with those monsters. Sure he could have beat a few of them but the odds would be stacked against hium.........It might take a big guy 10 tries and a very sore face before he could take Bruce down but if and when he did Game over..........The Gracies, Sakuraba great fightes of there time...........Sakuraba in his prime......Bruce in his.........would have been the best match since sliced bread was invented. Inside a gage Sakuraba would win outseide Bruce would have had the room to avoid him long enough to beat the crap out of him IMO.
No matter how good you think Bruce was........and he was a legend and a top MA above all even before he died, Martaial Arts is not magic.....there's no hidden secrets and even Bruce's 1 " punch was just a demonstation gimic........guys never in stance when he does it said it would hurt them too much lol..course it would hurt but wouldn't knock the guy on his ###.
I have only seen Bruce fight once in footage and boy he was fast, stylish and took a guy down so fast it would make your etes water.......other than that there are a few training movies going around with James Coburn and he messing about.
But if you want to see the real Bruce Lee try and get a hold of the take outs when he was making Game of Death..........He smacks himself on the head with his nunchakas.........messes up fight scenes all sorts........Guys was a very talaneted MA but you only need to watch Kick Boxing live or on Tv to realise it's nothing like Bruce Lee , Jet Li etc on screen.
One final thing before i go someone said Steven Segal was more of an actor than a MA.
Someone slap that boy

Big Steve in his early days was one of the best MA in the world...has hands the size of shovels...he was and still is the real McCoy and not many would stand in his way and be there for long...hamburgers or not....He has one of the hardest student gradings in the worls today and can do things other MA would only dream off.............Jet Li was and still is nothing morse than a Kata expert, JCV Dammne......fit but was never any sort of champion.....Wesley Snipes truly another excellent high calss MA and one real tough dude in real life. Jackie Chan..no more than a 1st dan in hapkido but a great gymnast. Only one I would give a chance to against MMA was big Steve..........even more than Bruce himself.