Nearly all visual representations of Bloom, beginning with Joyce's own pencil sketch in 1926, portray him with a mustache (one notable exception is Milo O'Shea's splendid performance in Joseph Strick's 1967 film), but one must dig long and hard in Ulysses to find any hair on the protagonist's upper lip. (A hint: the first twelve chapters will disappoint.) The universal impression has primarily been created, it would appear, by the book's references to a "moustachecup, sham crown Derby," that, according to Calypso, Milly Bloom gave her father as a birthday present: "Only five she was then. No, wait: four," an age confirmed in Ithaca. (Doubtless her mother assisted in the selection.)
Mustache cups were a fixture of Victorian tea drinking. They originated in England in the second half of the 19th century, in response to a decades-long love-affair with mustaches. A ledge inside the cup, separated from the brim by a small opening, kept messy liquids off gentlemen's lip hairs and prevented their heat from melting the wax that some used to keep those hairs impeccably coiffed. Crown Derby ("Royal Crown Derby" after 1890, by proclamation of Queen Victoria) was a prestigious brand of fine porcelain made in Derby. Molly and Milly have evidently economized by purchasing a less expensive "sham" knockoff. Ithaca makes clear that the gift came with a "saucer of Crown Derby" as well.
The spirit in which Bloom honors his loving daughter's gift is one of the homely glories of Ulysses. Ithaca notes that no one else in the Bloom household may use the mustache cup, but Bloom comically yields his "symposiarchal right" to Stephen when he serves his guest cocoa. This sentence goes on to introduce a mystery, however. It says that after giving Stephen his patriarchal cup "he substituted a cup identical with that of his guest" for his own use. Was the birthday cup one of a set? Did Molly select one for Milly to present to her father? How do people tell the special one apart from the others?
It is interesting that the novel almost never places a mustache on Bloom's face, because it does so to other men frequently and with confident, colorful brushstrokes. Mr. Deasy seems to be led about by his whiskers: "He turned his angry white moustache," "Blowing out his rare moustache." Simon Dedalus' handlebars are likewise animated: "his angry moustache," "blowing out impatiently his bushy moustache," "tugging a long moustache."
On some men, the display is prodigious. Molly's father Brian Tweedy had "big moustaches," "moustached like Turko the terrible." Dennis Breen's father had "large profane moustaches"; there was a "Picture of him on the wall with his Smashall Sweeney's moustaches." Father Cowley seems to be losing a battle for control of his face: he "brushed his moustache often downward with a scooping hand." The anonymous eaters in the Burton restaurant have trouble keeping theirs out of their food; they are seen "wolfing gobfuls of sloppy food, their eyes bulging, wiping wetted moustaches." But some attentive curation can keep the things under control. Gerty MacDowell's Prince Charming will have "glistening white teeth under his carefully trimmed sweeping moustache." Bartell d'Arcy appears a "Conceited fellow with his waxedup moustache."
Other men cultivate a more spartan look. M'Coy stands "picking at his moustache stubble," and Bloom notices that Bantam Lyons has "Shaved off his moustache again, by Jove! Long cold upper lip. To look younger." Seymour Bushe had a "foxy moustache." Tom Kernan thinks his "Grizzled moustache" makes him look like a soldier. Of the two soldiers that Molly has consorted with, one or the other, Mulvey or Gardner, had a mustache; Molly can't quite remember which.
Even women's mustaches come in for narrative attention. Like Nora Barnacle, Cissy Caffrey one night "dressed up in her father's suit and hat and the burned cork moustache and walked down Tritonville road, smoking a cigarette." Bella Cohen "has a sprouting moustache," and when she becomes Bello we see "fat moustache rings round his shaven mouth." Molly thinks that swallowing semen isn't so bad, "only thats what gives the women the moustaches."
In this lush tropical forest of Dublin mustaches, Bloom's barely registers. The only sentence in the entire novel that clearly suggests he has one is Gerty's visual impression of the man sitting across from her on the strand: "She could see at once by his dark eyes and his pale intellectual face that he was a foreigner, the image of the photo she had of Martin Harvey, the matinee idol, only for the moustache which she preferred." Is Bloom the one with the mustache? In context almost certainly yes, and in fact definitely so (as contemporary photographs of Harvey demonstrate), but the ambiguity in this, the sole clear indication that Bloom sports a mustache, shows just how little Joyce cared to draw attention to the fact.
In Circe Henry Flower "has the romantic Saviour's face with flowing locks, thin beard and moustache," but clearly the majority of these features are not to be attributed to Bloom himself.