If anything, he's a whiny brat. Always wanting to beat Mega Man, always wanting to become the strongest robot, that's all he ever thinks about. Granted that's exactly what he was programmed to be like, he never really thinks about how to come about it, and just keeps trying to beat'em up. Never going up to Wily and saying "Hey, gimme powers to beat Mega man" or no thinking of plans to bring about Mega Man's downfall and make him weaker, he just wants to beat him with his own two hands. Granted that's pretty admirable of him to only rely on himself, the problem lies in that: he relies ONLY on himself and sometimes Treble. Mega Man has Rush, Dr. Light, Roll, and Beat and reasons to protect them, something Bass doesn't have or understand, so it ends up being a "I fight for my friends thus giving me power" shtick.
tl;dr, Bass' character flaw of being solo makes him a loser and whiny brat.