Wordorigins.org

One of the mysteries of the game of baseball is the origin of the term bullpen, the name for the area in which relief pitchers warm up. Several competing theories vie for the origin. About all we know for sure is the earliest recorded use of the term to refer to the pitchers’ warm-up area was not until 1915, in Baseball Magazine in the article “Baseball Terminology” by Edward Nichols.  Another 1915 use is from Lester Chadwick’s Baseball Joe in the Big League:

He took the ball, and nodding to Rad, who was not playing, went out to the bullpen.