The title promises a nursery rhyme, and the poem borrows its bounce: short lines, a repeated "I went," a neat swan-to-swan echo. But what happens underneath is stranger and less innocent than the sound suggests.
The speaker moves from an ordinary office to a palace, as if work and power were one continuous journey. "A swan to the swan" suggests a kind of mirror or match, perhaps someone fitting perfectly into a grand, graceful world, or perhaps only seeing their own image there. Then the tone shifts. A bull in a chamber is a wild, heavy presence in a delicate room, and rattling the crown sounds like irreverence, even a threat. Judging by these images, the speaker seems playful but defiant, enjoying the disruption of authority.
The mood is mischievous and slightly menacing, like a children's game with an edge of rebellion.