Milly does not actually appear in Ulysses, except in the thoughts of Leopold and Molly and in the somewhat indiscreet gossip of the young Alec Bannon. She is fifteen years old, and Molly and Leopold (Leopold being the dominant voice) have decided to send her to study photography in Mullingar, where she is living. It's there that she met Bannon, who appears in "Oxen of the Sun" hoping to buy condoms before he heads back to see her.
Since the death of their son Rudy, Milly is the Blooms' only surviving child. Leopold dotes on her, and remembers her with great affection. In "Calypso," both Leopold and Molly receive correspondence from Milly, but Leopold gets a whole letter whereas Molly only gets a card. In "Penelope," it becomes clear that there is some level of tension between Molly and Milly. Molly appears jealous of her daughter's beauty and popularity among young men, and suspects that Leopold only sent her off to Mullingar because he could see the affair with Boylan coming. As we learn throughout Ulysses, we can't really trust any of these perspectives and hence know pretty much nothing of Milly Bloom. Her parents' reflections on her are more notable for what they say about Leopold and Molly than they are for what they say about Milly.