Bishop can write some mean structured poems when she feels like it, but this one is a true free verse poem, since it doesn't follow any consistent rhyme structure or meter.
The poem is very balanced with six stanzas of eight lines each. The lines lengths are not as even as many of Bishop's other works, which gives us a hint that this is a poem from her earlier career.
Each stanza presents a different idea or stage in the Man-Moth's daily life. We begin by seeing the world without the Man-Moth, but then he appears, and we move through his hesitation before he bursts into action and ultimate failure in the third stanza. Next, we follow him underground, and then watch him on the subway until we are finally pulled in to become part of the story ourselves, since the final stanza uses the second person (you) point of view.
Overall, the poem has a very full look on the page. The lines are quite a bit longer than most of Bishop's other well-known poems (take a peek at "The Fish" or "The Moose" for comparison). The epigraph comes in handy when trying to figure out why she decided to get so long-winded for this one. The inspiration came from a newspaper, so maybe Bishop is trying to create a feeling of prose for this poem, like a dramatic piece in a newspaper. "The Fish" and "The Moose" are about single moments with a single animal. However, "The Man-Moth" is a story of a whole night and a creature with more depth than a fish or a moose. The poem feels more substantial because the subject is more substantial than just a fleeting moment. The poem is telling us a story, so it takes on a more story-like form.