OK, this one I saw around 1987 but the genre was pretty expansive between the mid 70s and 80s. That with the fact that my brother was an avid kung fu junkie… Makes me think it could have been nearly any kick flick. But I am fairly certain that the Bruce here was Bruce Li as he’s the only clone that I have mistaken for THE Bruce.
The plot as far as i can recall: Bruce (not portraying Lee in this one) is training under an old guru type when he makes deadly enemies with a rival clan. The clan leader kills bruce’s mentor. But he tells bruce in his dying breath that snake style will defeat the guy who bested him. Then there’s a training montage of bruce practicing his snake style WITH SEVERAL COBRAS!!!! Throughout the mantage Bruce is drinking and occassiinally spitting out a clear liquid onto the snakes. As he was bitten several times, i assumed he was drinking some kinda antivenom, but maybe it was sake? How sake prevents poisonous venom from killing you, i have no clue… But it may explain seeing you arms turning into snakes.