The Bishop's hypocrisy is the poem's fundamental irony. This supposedly holy man, quick to spout familiar aphorisms about the brevity of life and the emptiness of worldly wealth, is in truth a money-grubbing, lustful, materialistic old sinner.
Everything this Bishop has done during his tenure in a supposedly selfless pastoral job has been in the service of his personal comfort. He’s used his wealth to build countless country houses, stolen treasures from his own church, and fathered a substantial clan of illegitimate children. To him, being a Bishop just means having easier access to wealth, power, and pleasure.
He even behaves as if his church’s patron saint, St. Praxed, is just another higher-up he can pull strings with: he offers to put a good word in with her for his sons if they follow his tomb designs to the letter. In short, if this Bishop ever really believed in his religion or cared for his congregation, there’s absolutely no sign of it in his behavior.
Not only does the Bishop fail to live by the tenets of his religion, he can’t even die by them. Without real faith, he can take no comfort in the thought of a Christian afterlife. His obsession with his splendid tomb is a cover for his fear of death: whenever he begins to ponder his mortality, he quickly turns his mind to semiprecious stones and elaborate sculpture instead. He can’t even seem to face the bare facts of death, instead imagining that he’ll just lie cozy in his church enjoying “the blessed mutter of the mass” for eternity. His hypocrisy doesn’t just make him a corrupt and selfish man, but a cowardly and delusional one as well.
The deep irony here, then, is that the very man whose job it is to teach love, selflessness, faith, and generosity possesses none of these qualities himself.