This short poem is described as having been written into the marigins of the Red Book. It is supposed to depict a hobbit's idea of what an elf-maiden is. A precursor of the poem, called The Princess Ni, was published in the collection Leeds University Verse 1914-24.
For the second poem in this publication, Tom is yet again the main character. This time the reader follow him on a boating trip along the Withywindle and his journey to meet Farmer Maggot. In this story we encounter familar places in Buckland and the Shire. The idea is that the events set out occured some time after Frodo and the other Hobbits visited Farmer Maggot and Tom Bombadil and that the poem is composed by Buckland hobbits.
The Adventures of Tom Bombadil and Other Verses from the Red Book contains 16 poems, each with their own plot. It was first published in 1962. I have read a 2014 edition of the book, edited by Christina Scull and Wayne G. Hammond. It contains extra content, such as earlier versions of the poems, and commentary.