The nameless "White slip of paper" that Bloom checks in Calypso, to make sure that it is "Quite safe" inside the leather sweatband of his hat, figures more prominently in Lotus Eaters. There, it turns out to be not really a slip of paper but rather a "card"—what Victorians and Edwardians called a "calling card" or "visiting card," the equivalent of our "business cards" today. Bloom presents it at the post office to collect mail from his erotic pen pal Martha Clifford, under a pseudonym. Before entering the post office, in a performance calculated to remove any suspicion about his clandestine correspondence he moves the card from his hat to a pocket of his vest. It is one of several moments in the book when Bloom sees himself as others might and takes ingenious and probably excessive precautions to hide his intentions from them.
The first-time reader of Calypso cannot know what to make of the paper, other than to note that Bloom thinks he has hidden something well. Lotus Eaters reveals the card's true nature when Bloom hands it "through the brass grill" of the post office window, asking "Are there any letters for me?" When he reads the envelope that is handed to him, it becomes clear that he carries in his hat a card bearing the name "Henry Flower, Esq." The calling cards of the day sometimes bore simply the person's name, and sometimes added an address. Henry lists his address as the Westland Row post office box.
Bloom, then, has invented a respectable alias to cover his epistolary affair; he has set up a postbox for the fictive Henry at a site far removed from his own neighborhood; and he has apparently had cards printed to avoid having to pronounce the name Henry Flower in a public setting where someone who knows that he is not Henry might hear him saying it. To make even more sure that he will not be detected, before entering the post office he checks to see that there is no one but the postmistress in the lobby: "From the curbstone he darted a keen glance through the door of the postoffice. Too late box. Post here. No-one. In."
Nor is that the end of his Odyssean cunning. While he is still across the road from the post office he enacts an elaborate charade to move the card, by sleight of hand, to a place that a respectable gentleman might keep such an item: "he took off his hat quietly inhaling his hairoil and sent his right hand with slow grace over his brow and hair. Very warm morning. Under their dropped lids his eyes found the tiny bow of the leather headband inside his high grade ha. Just there. His right hand came down into the bowl of his hat. His fingers found quickly a card behind the headband and transferred it to his waistcoat pocket." Once more he thinks, "So warm," and (in a Gabler textual emendation that makes much better sense of the following sentences and is adopted on this website) he once more passes his hand over his brow and hair and returns the hat to its rightful place.
Of this remarkable performance, Peter Kuch writes in Irish Divorce: Joyce's Ulysses (Palgrave Macmillian, 2017) that "It is now eleven o'clock, and it is warm but not hot. But by pretending it is 'rather warm,' Bloom devises a sequence of gestures that will conceal what he is actually doing—that is, transferring the card from his hat to his waistcoat. All his gestures become self-consciously choreographed. . . . What had been a quick and somewhat furtive action before breakfast has become, barely an hour later, a subterfuge that is as complex as it is self-consciously orchestrated, performed meticulously as it were before a wholly imagined audience" (75).
A smaller but very similar charade in Lestrygonians shows Bloom disguising his intentions not to preserve his sexual reputation but to guard against offending others. In their defensiveness both passages seem to anticipate the hallucinations of Circe, where Bloom is repeatedly accused of doing shameful things.