Psycho is from ancient Greek for spirit, mind, or mental. Psycho Power is also what Bison calls the dark perversion of Soul Power that he quite very likely pioneered. Meaning that Bison is the first “Psycho Power” wielder in history.
More or less true but it would help explain a lot of the otherworldly nature of the character, and a lot of his dialogue.
He is essentially an immortal god of war/agent of chaos-type character. It’s not as esoteric or far fetched as it seems at first glance. If you dig deeper you will see it actually a legitimate basis in the canon, albeit subtly presented.
I think ultimately, the truth is somewhere between both theories:
Bison is an older-than-you-think Nazi-esque fighter with a military background who forged his own path to the top of the food chain when he unlocked the dark potential of a rare mystical martial art he was studying. At some point, he decided to take his Military expertise and combine it with the essence of Psycho Power (fear, despair, hate) to will into existence an Order that will bring about chaos, anywhere anyhow. Why? To become the strongest of all of course! Who needs world domination?!
Somewhere along the way, he ceased being human when his powers grew strong enough to subjugate nature itself to his will. But while he may have lost his humanity (willingly obliterated every trace of it is more apt), he never lost his sense of humor and irony, even in face of the Absurdity of the SF universe.