As early as 1809, the term bullpen referred to a stockade for holding criminals.
In the 1870s, a roped-off area in the outfield for standing room was nicknamed the bullpen by the Cincinnati Enquirer.
When relief pitchers were introduced into the game they took over that area to warm up.
In a stroke of brilliance the Bull Durham Tobacco Company erected a sign overhead to confirm it as the bullpen.
The warm-up area for baseball pitchers is called a “bullpen”.