[denethorthefirst]

I do not think that Goldberry is an Ainu (or one of the Ealar, for that matter, i.e. a naturally discarnate being), because it is stated that she has a mother (the "River-Woman"). My Head-Canon is that Goldberry is, like Luthien, the offspring of a Maia and an Elf. The "River-Woman" could be a female Maia of Ulmo that resided in that region of Eriador just as the Elves were passing through during the Great Journey or maybe she accompanied the Journey. Just like Melian with Thingol this unnamed River-Maia then fell in love with an Elf, incarnated herself for him and gave birth to Goldberry. What happened next is anybodies guess: maybe they both moved on after they grew weary of Middle-Earth or they got killed during the events of the First Age, either by one of the many of Melkors free roaming Monsters, or by the Creatures and Orks that fled Angband after its destruction and passed through Eriador on their way to the East. Whatever happened to the parents, in the end Goldberry fell in love with Bombadil and stayed with him.