Bloom gets much of his conception of the Middle East from romantic novels and Christmas pantomimes like Turko the Terrible, and he acknowledges that the real thing is "Probably not a bit like it really," but many of the details of his reverie in Calypso would seem familiar to a native of the region. Cold nonalcoholic drinks with fruit and herbal flavors are indeed sold as "sherbet" in Turkey, Iran, and Arab countries, as well as some lands farther east.
Several different kinds of sherbet are mentioned in the Persian medical encyclopedia Zakhirah-i Khvarazm'Shahi, which dates to the 12th century. The word itself is Arabic in origin: the root sh-r-b refers to drinks, and drinks of this type are called sharba in modern Arab countries (wine is sharaab, distilled liquor mashroob). In Iran they are sharbat, and in Turkey serbet. It is not clear what tongue Joyce may be thinking of when he has Bloom mention "their dark language," but Arabic, Persian, and Turkish all share this word.
West Asian sherbets are made by dissolving a sweet condensed nectar—made variously of fruits (cherry, lemon, strawberry, pineapple), flower petals (orange, rose, hibiscus), and/or seeds (basil, chia, anise)—in several parts of chilled water. Sherbets "scented with fennel" seem to be unheard of, though the similar-tasting anise is sometimes an ingredient. (Like the Greek ouzo and the Swiss absinthe, Turkey also has an alcoholic anise drink called raaki.)
In Iran sharbats are usually served elegantly in tall glasses, with long spoons for guests to stir the ingredients together, but in Turkey street sellers called serbetci dispense the liquid already mixed from brass flasks strapped to their backs. This may be the source of Bloom's fantasy of drinking sherbet while wandering the streets of a Middle Eastern city.
Thanks to Dr. Iman Fani for a personal communication of some of the information in this note.