I figure since he was a reporter his historical accuracy was probably on point, but im not sure.
Herbert Asbury's books have long been an important source for popular and narrative historians writing about the 19th and early 20th centuries, and they are also – in my view surprisingly – quite frequently cited by academic historians, but the reality is that they are anecdotal, romanticised and, when investigated, very frequently inaccurate to a sometimes quite alarming degree. What Asbury is selling are anecdotes and stories (with all that implies for the need for beginnings, middles and ends, heroes, villains, and satisfying moral outcomes). There is little to nothing in his books to root these in the social and economic history of the times and the problems I have encountered in trying to research and confirm specific materials in his works (both for published books on the Becker scandal in New York in the early C20th and the origins of the Mafia in New York and New Orleans in the late C19th, and for answers here at Ask Historians) have taught me to be very wary indeed of his claims.
Here is a link to a response I published regarding the accuracy (or lack of it) of Scorcese's film Gangs of New York, which is itself an inaccurate retelling of Asburys inaccurate claims regarding the gangs of the mid-nineteenth century. And here is a link to a response I posted a couple of years ago on the subject of shanghaiing sailors in San Francisco, a topic that figures prominently (and equally sensationally) in Asbury's book on the Barbary Coast.