Bombadil and Goldberry’s meeting is described in The Adventures of Tom Bombadil, and Other Verses from the Red Book, a collection of poetry relating to Middle-earth which was published in 1962. This is one of very few books about Middle-earth other than The Hobbit and The Lord of the Rings that was actually published by Tolkien within his own lifetime, rather than being edited and published after his death by his son Christopher. Amazon Prime Video and The Rings of Power do not have the rights to this book and so cannot refer to it directly, but it does confirm things that are implied in The Lord of the Rings, which they do have the rights to: Bombadil and Goldberry are married, and she is the daughter of the river Withywindle. (The poem also describes how Goldberry grabbed Tom and tried to drown him, and later he grabbed her and carried her off to be his wife, so it may be something of a blessing that the show does not have the right to adapt that part!)
One of the odd things about Goldberry’s appearance in The Rings of Power is that she is a very long way from where we would expect her to be. Bombadil himself, whatever he is, could easily be wandering about various parts of Middle-earth back in the Second Age. At the Council of Elrond in The Fellowship of the Ring, Elrond specifically says that Bombadil “walked the woods and hills long ago,” and Gandalf adds that he “is withdrawn into a little land,” implying that he is did always stay in his small part of the lands near the Shire, and used to travel more. So finding Bombadil in Rhûn in the Second Age does not contradict anything we know about him.
Goldberry, however, is implied to be the daughter of a specific river, the Withywindle. This is a small river that runs from the Barrow-downs through the Old Forest, on the borders of the Shire, to merge with the Brandywine River. Tolkien is even less specific about her exact nature than he is about Bombadil himself, but he implies that she has a need for water and a love of water-plants, hence the bowls of lilies around her feet, and a deep connection with rain, rivers, and water in general. So what on earth is she doing in the desert?
Goldberry’s inclusion in The Rings of Power is rather a surprise. We had assumed, when Bombadil’s appearance was announced, that this would simply be a story that took place before they got married. Marrying Goldberry could even be assumed to be the reason Bombadil withdrew into a small area of land near the Withywindle. It is true that, as a river-spirit, there is not much indication of how old she is and she could certainly be around in this period, but since she is so strongly bound to a specific river near the Shire, we were not expecting to see her so far away from it.
And of course the other odd thing about her appearance in the show is that we do not actually see her at all. The Stranger is in the bath at Tom’s house and hears Tom singing one of his songs from The Lord of the Rings. Viewers clearly hear him say, “Don’t be bashful now Goldberry,” and a woman’s voice joins him in the song. Then a pot rattles and Bombadil comes in with the Stranger’s robe. When the Stranger asks Bombadil if there is somebody out there with him and says he thought he heard a woman singing, Tom bizarrely replies, “Woman? What woman?” When the Stranger tries to clarify, “is no one else here with you?” Bombadil unhelpfully confirms that, “you’re here. That is, I think you are,” and laughs. And that is the end of that. There is no indication of why he is being so cagey about his wife, no simple explanation that she is shy, and the subject is never brought up again.
Goldberry is voiced by singer/songwriter Raya Yarbrough, who is married to series composer Bear McCreary and has collaborated with him many times. Her voice will probably be most familiar to viewers from her rendition of the re-worked Skye Boat Song from the opening titles of Outlander, for which McCreary is also the composer. Other than being a beautiful voice, the notable thing about her casting here is that she is a singer, not an actress, which implies that we will not actually be seeing Goldberry on screen in this series.