The title gives the joke away: this is a church of sloth, where the faith on offer is doing nothing. The first image is a quiet, ordinary church with men in hats "blessing without waking." That last phrase is the funny, slightly sly part. The blessings seem automatic, performed half-asleep, as if religion has turned into a drowsy habit. It could describe a sleepy congregation, or priests going through the motions, or both.
Then the speaker steps in. "I bury my pen" suggests giving up work, specifically the work of writing, and "pray to Bed" makes the capital letter do the joke. Bed becomes the god this speaker truly believes in. The tone is playful and self-mocking rather than bitter. The speaker isn't attacking the church so much as admitting that comfort and rest are more tempting than either duty or devotion. The mood is hushed, lazy, and a little mischievous, like a yawn with a grin in it.