Martha Clifford is a woman who responded to an ad of Bloom's in the paper requesting a typist. The two of them have begun writing letters to each other full of sexual innuendo, though by most standards they are pretty tame. In "Lotus Eaters," Bloom picks up a letter from Martha in which she calls him a naughty boy, says she wants to meet, and asks what kind of perfume Molly wears. He thinks about her throughout the day, and answers the letter in "Sirens." In "Circe," Martha appears in one of Bloom's dreams. She is crying and calls him a lewd man.
Bloom's correspondence with Martha Clifford is one of his small marital infidelities, but it is clear that Bloom could never actually consummate the affair.