The Wildcats' senior right-hander allowed four runs -- three earned -- on six hits and a walk through only 3.1 innings as UK fell behind early and could never catch up. Cody also hurt himself with a throwing error and a wild pitch.
No. 22 Kentucky (3-3) had nine hits, including a two-hit game from sophomore shortstop Riley Mahan, but could not cash in on enough of its scoring opportunities.
Bryant starter James Davitt (1-0) worked into the sixth inning, allowing just five hits and two runs with seven strikeouts and no walks. Logan Lessard worked the ninth for the save, his third of the year.
The Bulldogs (6-1) got a three-run homer from outfielder Nick Angelini, while designated hitter Brandon Bingel added three hits and two RBI.
Kentucky returns to action on Wednesday, playing host to Austin Peay in the home opener at 4 p.m. ET at Cliff Hagan Stadium.