Cartoonist Willard Mullin of the New York World-Telegram was famous for his cartoons of the Brooklyn bum. He allegedly first created the Brooklyn bum in 1937.
I found the first Brooklyn "bum" slightly earlier, in the Brooklyn Eagle I believe. My work is in the old archives of the American Dialect Society, which are now no longer available. So much for sharing your work with scholars.
Below are a few citations. The full-text Sporting News didn't provide any early citations.
14 March 1939, Wisconsin Rapids Daily Tribune, pg. 5, col. 3:
Two days later, Red pitchers held the Dodgers hitless...Some of the comment on the no-hitter: New York Mirror - "This has got to stop"; Post - "Dodgers alread in mid-season form"; Flatbush fans - "Dem bums"...
11 September 1940, Washington Post, pg. 19:
We asked our taxi driver about it this morning. What did he think about the pennant race? How about the Indians? He cocked his head over his shoulder in our direction and looked at us balefully.
"Dem bums," he said, "are bums."