“Dixie Walker warmed up in the bullpen with Groom, but was saved for tomorrow’s game.” Washington Times, May 19, 1912, p16.
“When Tesrau began to cave he went fast, and after Wagner and Cady had hit safely in the seventh McGraw sent Marquard down to the bullpen to warm up, but he switched and picked Crandall to go to the mound.” Walter Johnson, Washington Times, October 9, 1912, p14
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1913. “Ira Thomas is the skipper of the [Athletics] pitchers. He corrects the faults of the youthful trajectory hurlers and takes them to the ‘bullpen’ in the afternoon and keeps them warmed up” (The Washington Post, Aug. 17; Peter Morris).