(Oxford English Dictionary)
b. attrib., in sense 'of, pertaining to, or characteristic of the Bowery'; Bowery boy, a rough or rowdy of a type at one time characteristic of the Bowery.
1840 Daily Picayune (New Orleans) 28 Aug. 2/1 The Bowery boys of New York have..eclipsed the nice young men of Baltimore. 1852 C. A. BRISTED Upper Ten Thousand 29 Its occupants are of not-to-be-mistaken Bowery cutveritable b'hoys.
From Irving Lewis Allen's City in Slang (1993), pg. 210:
The famous Bowery Boys, often just the boys, were a loosely organized gang associated with Bowery life from about 1835 to the 1850s. Many became volunteer firemen and in those days were as famous for fighting other gangs of firemen as for fighting fires. Stuart Berg Flexner explained that "when one referred to such a Bowery Boy the fad was then to use a contemptuous or humorous mock Irish pronunciation of 'Bowery B'hoy.' A Bowery Boy's girlfriend or female counterpart was called a Bowery Girl, often pronounced 'Bowery Ga'hal.'"
Did "Bowery Boy" - like "the Big Apple" - come from horseracing?
16 September 1829, Adams Sentinel (Gettysburg, PA), pg. 3, col. 3:
Great racking match and unprecedented speed. - On Monday afternoon, at half past 1 o'clock, a race was run on Long Island Course by the celebrated horses, Bowery Boy and Stranger. The distance was two miles and repeat. The first heat was racked in five minutes and 4 1/2 seconds - the second in 5 minutes, 7 seconds. Both heats were won by Bowery Boy - the first with ease, the last by a short distance. At a former race, Stranger was the winning horse. Balt. Gaz.
The “celebrated” horse Bowery Boy was mentioned in a NYC newspaper a bit later in 1829: Commercial Advertiser, October 5, 1829, p. 2 col. 5; he was described as a “racking” horse—this was not a typo for “racing”, and was a category mentioned together with trotting and pacing.