The baseball terms “major league” and “big league” refer to the top professional league; these terms have been used outside of baseball as well, with a similar meaning. “Bush league” is a “minor league” that is below that. The “bush” term has not been explained completely in print in an early citation, but “bush” implies an insubstantial plant (or thing). The baseball “bush leagues” were usually located in rural areas.
 
“Bush league” has been cited in print since at least 1896.
   
     
MLB.com
Bush League
Definition
“Bush league” describes something that is below professional standards.
Origin
With “bush” being a synonym for a rural area, non-Major League clubs in small towns were referred to as bush league teams in the early days of baseball. The term has come to be used often outside of baseball.
 
Wiktionary: bush league
Noun
bush league (plural bush leagues)
1. (chiefly US, idiomatic) A professional sports association at the lower levels of minor league organization.
2. (figuratively, by extension) A low-ranking or inferior level among groups, professions, organizations, etc.
 
(Oxford English Dictionary)
bush league  n. Baseball a minor league, esp. one of mediocre quality; frequently transferred and attributive.
1906 [see bush leaguer n. at Additions].
1908   Baseball Mag. July 79/2   Being from Chicago, that bush league town wasn’t good enough to hold Hermaine’s sandals.
1914   ‘High Jinks, Jr.’ Choice Slang 8   Bush league trick, a trick indulged in which is not in harmony with its surroundings
       
Newspapers.com 
13 January 1896, St. Louis (MO) Globe-Democrat, pg. 9, col. 3:
LEAVES THE ST. LOUIS BROWNS.
Theodore Breitenstein Will Pitch for Chester, Illinois, in 1896.
(...)
“But I could not get my price here, and, as I could not go to any club playing under the national agreement, I must go into a ‘bush’ league.”
 
15 January 1896, Rockford (IL) Daily Register-Gazette, “Sporting,” pg. 7, col. 5:
The Southern Illinois league consists of Belleville, Cairo, East St. Louis, Springfield, Edwardsville, Chester and Sportsman’s park. St. Louis. It is a “bush” league, outside the pale of a national agreement.
 
6 March 1896, Rockford (IL) Daily Register-Gazette, pg. 3, col. 4:
BASE BALL NOTES
Theo. Breitenstein, the crack southpaw pitcher who has made a big bluff about playing in a little illinois “bush” league, has at least signed a St. Louis contract.
   
Newspapers.com
21 June 1899, Buffalo (NY) Evening News, “Grem Got Next,” pg. 6, col. 1:
And not the least of the changes and perhaps the most unexpected was the advent of Hausen in the former “Bush League,” who caught Earnest Danny Daub’s benders and shoots.
 
Newspapers.com
5 August 1899, Detroit (MI) Free Press, “The Canadian Pitcher,” pg. 6, col. 1:
According to all accounts from London, Ont., the Tigers played yesterday much as they did in the exhibition game over in the queen’s domain, and if a trip to the bush league is to have the effect of inoculating the Western leaguers with that style of work, such excursions should be tabooed in the future.
   
Newspapers.com
21 June 1901, The Daily Argus-Leader (Sioux Falls, SD), “Late Local News,” pg. 8, col. 3:
Beall got scared at the idea of a bush league team beating his leaguers and called the game off.
 
OCLC WorldCat record
The Young Phenom.A YOUNG phenom in a bush league grew, Whose
Edition/Format: Article Article
Publication: Frank Leslie’s Weekly, (MARCH 3, 1910)
 
OCLC WorldCat record
Bush league: a history of minor league baseball.
Author: Robert Obojski
Publisher: New York, Macmillan [1975]
Edition/Format:   Print book : English
 
Newspapers.com
3 April 1988, Star Tribune (Minneapolis, MN), “A bush leaguer’s glossary of terms,” Sunday Magazine, pg. 9, col. 3:
Bush leagues: Elizabethton, Paintsville, Visalla, Lynchburg, Shreveport and all the other wonderful minor-league towns that many of the Twins hop never to see again.
     
Urban Dictionary
Bush league
Also see Bushleague. Adj. 1) Below good standards, not good or incorrect. Pitiful, poor, terrible, awful, bad, sucky,
“That’s a bushleague call, ref.”
“That kid is real bushleague.”
by Better Than You March 26, 2005
 
OCLC WorldCat record
Bush League boys : the postwar legends of baseball in the American Southwest
Author: Toby Smith
Publisher: Albuquerque : University of New Mexico Press, 2014.
Edition/Format:   Print book : Biography : State or province government publication : English : First edition
Summary:
This loving tribute to the defunct minor league teams of New Mexico and west Texas resurrects a forgotten period of baseball history. Through oral histories of players, umpires, fans, sportswriters, and team officials, Toby Smith brings to life the West Texas-New Mexico League, the Longhorn League, the Southwestern League, and the Sophomore League from 1946 to 1961, when the last of them folded. Star players Joe Bauman and Bob Crues get special attention, along with assorted brawls, a fatal beaning incident, home runs, and marriages conducted at home plate. Anyone who loves baseball will enjoy this delightful book.—Amazon.com