Abso-fucking-lutely nothing to do with auto racing, or anything else some functionally illiterate hillbilly might suggest. Popular usage of the phrase pre-dates that example by many decades. It's rooted in baseball, refers to leagues considered to be inferior to the majors, and is purely coincidental that it shares a spelling with our 43rd President.
Dumbass rednecks trying to correct spelling is fucking bush league, man.
to denote a sub par level of competition or gameplay.
What's this bullshit?! I don't fucking care! It don't matter to Jesus! But you don't fool me! You might fool the fucks in the league office, but you don't fool Jesus! It's bush-league psych-out stuff! Laughable, man! Forced laugh I would've fucked you in the ass Saturday. I'll fuck you in the ass next Wednesday instead! Wooo! You got a date Wednesday, baby!
A phrase commonly used in (but not restricted to) baseball to describe something (usually a playing style or attitude) that is not respectable or sportsmanlike, but technically not breaking any rules of the game. Someone who commonly plays with antics that are considered bushleague, would be considered a "bushleaguer". Both "bushleague" and "bushleaguer" can also be used to describe unsportsmanlike acts by fans, and to describe the fans themselves, respectively.
BATTER: "Aww cmon ump, are you gonna let the catcher get away with that?? He keeps taunting me as the pitch comes in. This is such Bushleague crap.
UMPIRE: "I don't wanna hear any more of it. Now get in the box and shut your mouth."