The irony of B. Wordsworth's interest in the boy
Though his exact age is never identified, readers know that B. Wordsworth is an older, perhaps middle-aged man. Apart from their own children and other associated families, most men that age have no interest in cultivating a relationship with a child like a boy. B. Wordsworth, however, wishes to (and ultimately has) a relationship with the boy, a relationship which is both strange and unexpected.
The irony of the boy's mother
Few adults would allow a strange man well into his middle years who has no relation to their family to have a relationship with a young boy. Even fewer would allow that child to go to the man's house. The boy's mother, however, allows her son to go to B. Wordsworth's house, an action that is wholly unexpected and peculiar given the circumstances.
The irony of B. Wordsworth's intrusion into the boy and his mother's home
The boy and his mother live a seemingly normal and tranquil life. However, the boy's mother allows a man she does not know (and who is a beggar) to enter her home and interact with her son so that he could see the bees the woman had. Such an action flies in the face of rationality and societal norms. After all, few people would allow a stranger to enter their home. Even fewer would allow a stranger into their home if they were a beggar without a home. And even fewer would allow someone to enter their home and interact with their small child alone.
The irony of B. Wordsworth's profession
B. Wordsworth is a poet—or at least he claims to be one. Any artist who does not make money (especially someone who has made no money) in their craft would either abandon said craft (whether it be writing, sculpture, drawing, painting, etc.) or get other employment so that they could support themselves. B. Wordsworth does neither. Instead, he leeches off people in his life and on the generosity of other people in his orbit.
The irony of the "greatest poem ever written"
B. Wordsworth consistently exclaims to the boy that he is in the process of writing the "greatest poem ever written." He is writing this poem, Wordsworth explains, at a pace of one line per month. That poem, however, does not and will never exist. It is a fabrication and a figment of Wordsworth's imagination. Most artists think they have created something good and valuable. However, most artists have produced that work (or will eventually produce that work).