Holden does not like the bartender at the Wicker Bar because he regards him as a very insincere type who doesn't bother with the customers unless they're rich or famous. This snobbery and pretentiousness is characteristic of the whole place in Holden's view:
It's one of these places that are supposed to be very sophisticated and all, and the phonies are coming in the window. (chapter 19).
Phonies, of course, are to be found in every corner of society as far as Holden is concerned, but he does seem to reserve his greatest vitriol for people and places that aspire to being suave and cultured and elitist; for example his girlfriend Sally Hayes, who gushes over famous actors, and her even more insufferable acquaintance, an Ivy League type who bores Holden almost to death with his conversation. He is the sort that Holden visualises generally sitting around with his equally stuck-up friends, all of them 'criticising shows and books and women in those tired, snobby voices' (chapter 17).
Holden certainly does not denigrate art himself, nor does he altogether forego his visits to trendy hotspots, but he simply can't bear people who seem to him to just make a show of being artistic or knowledgeable.
J.D. Salinger's model of youthful alienation, Holden Caulfield, has little good to say about many of the people he has encountered in his relatively brief but somewhat adventurous life. Part of Holden's sense of alienation emanates from a perspective of humanity dominated by pretentious, ignorant snobs. At one point in The Catcher in the Rye, Holden, bored and seeking some measure of human companionship during his sojourn to New York City, decides to contact an old acquaintance named Carl Luce, about whom Holden less than charitably recalls not liking "too much," but whose intellect was sufficient so as to merit an attempt at a reunion of sorts. To further emphasize Holden's disdain for the individual he now seeks out for intelligent conversation, he further notes that "I once called him a fat-assed phony."
This reference to Carl Luce as a "phony" is no mere aside. On the contrary, it encapsulates Holden's condescending approach to even those with intellects he actually respects. It also serves as a useful segue to the issue of the bartender at the Wicker Bar. It is at the Wicker Bar that Holden anticipates meeting up with Carl. In discussing the bar, Salinger's narrator notes that it used to serve as a regular hangout for him, but no longer serves that purpose because of the establishment's association with phoniness:
"I used to go there quite a lot, but I don't any more. I gradually cut it out. It's one of those places that are supposed to be very sophisticated and all, and the phonies are coming in the window."
Holden holds the Wicker Bar's bartender in particular disdain for the latter's objectionable demeanor—a demeanor that involves a large degree of obsequious behavior toward the bar's higher class clientele. In the following passage, Holden explains his attitude towards the bartender at the Wicker Bar:
"The bartender was a louse, too. He was a big snob. He didn't talk to you at all hardly unless you were a big shot or a celebrity or something. If you were a big shot or a celebrity or something, then he was even more nauseating."
Holden dislikes the bartender because the latter represents everything the former holds in contempt. The snobbish demeanor, the obsequious approach toward those he holds in higher esteem, and the bartender's phoniness are all reasons for Holden's dislike of this particular character.