Question: when was the book by J.R.R. Tolkien that Bilbo Baggins is the title character and protagonist originally published?

Context paragraphs:
The Road Goes Ever On (song): "The Road Goes Ever On" is a title that encompasses several walking songs that J. R. R. Tolkien wrote for his Middle-earth legendarium.  Within the stories, the original song was composed by Bilbo Baggins and recorded in "The Hobbit".  Different versions of it also appear in "The Lord of the Rings", along with some similar walking songs.

The Quest of Erebor: "The Quest of Erebor" is a work of fantasy fiction by J. R. R. Tolkien, posthumously published by his son Christopher Tolkien in "Unfinished Tales" (1980).  This work explains how and why Gandalf arranged for the retaking of the Lonely Mountain ("Erebor" in Sindarin), an adventure recounted from the perspective of Bilbo Baggins many years before in Tolkien's "The Hobbit".

Bilbo Baggins: Bilbo Baggins is the title character and protagonist of J. R. R. Tolkien's 1937 novel "The Hobbit", as well as a supporting character in "The Lord of the Rings".  In Tolkien's narrative conceit, in which all the writings of Middle-earth are translations from the fictitious volume of "The Red Book of Westmarch", Bilbo is the author of "The Hobbit" and translator of various "works from the elvish" (as mentioned in the end of "The Return of the King").

Smaug: Smaug ( ) is a fictional character and the primary antagonist in J. R. R. Tolkien's 1937 novel "The Hobbit".  He is a powerful, fearsome dragon who invaded the Dwarf kingdom of Erebor 150 years prior to the events described in the novel.  A group of 13 Dwarves mounted a quest to take the kingdom back, aided by the wizard Gandalf and the Hobbit Bilbo Baggins.  Smaug is described as "a most specially greedy, strong and wicked wyrm".

The Hobbit (1985 film): The Hobbit (full name The Fabulous Journey of Mr. Bilbo Baggins, The Hobbit, Across the Wild Land, Through the Dark Forest, Beyond the Misty Mountains.  There and Back Again, Russian: Сказочное путешествие мистера Бильбо Беггинса, Хоббита, через дикий край, чёрный лес, за туманные горы.  Туда и обратно , "Skazochnoye puteshestviye mistera Bilbo Begginsa, Hobbita, cherez diky kray, chorny les, za tumannyye gory.  Tuda i obratno") was a 1985 Soviet film adaption of J. R. R. Tolkien's 1937 book "The Hobbit" by Vladimir Latyshev.

Mithril: Mithril is a fictional metal found in the writings of J. R. R. Tolkien, being present in his Middle-earth, and also appearing in many other works of derivative fantasy.  It is described as resembling silver but being stronger and lighter than steel.  The author first wrote of it in "The Lord of the Rings", and it is retrospectively mentioned in the third, revised edition of "The Hobbit" in 1966.  In the first 1937 edition, the mail shirt given to Bilbo Baggins is described as being made of "silvered steel".

Highly Illogical: Highly Illogical is an album which contains a collection of songs performed by "Star Trek" actor Leonard Nimoy.  Most of the songs were originally recorded in the 1960s.  The collection includes "The Ballad of Bilbo Baggins", which tells the story of J.R.R. Tolkien's book "The Hobbit", and has been immortalized by being included on various novelty compilations over the years.

The Hobbit: The Hobbit, or There and Back Again is a children's fantasy novel by English author J. R. R. Tolkien.  It was published on 21 September 1937 to wide critical acclaim, being nominated for the Carnegie Medal and awarded a prize from the "New York Herald Tribune" for best juvenile fiction.  The book remains popular and is recognized as a classic in children's literature.

The Ballad of Bilbo Baggins: "The Ballad of Bilbo Baggins" is a song composed by Charles Randolph Grean and performed by Leonard Nimoy, telling the story of Bilbo Baggins and his adventures in J. R. R. Tolkien's novel "The Hobbit".  The recording was featured on "Two Sides of Leonard Nimoy," the second of Nimoy's albums on Dot Records.  It was also released as a single (Dot Records Cat.  #45-17028) in July 1967, backed with a "modern thought-image" folk song called "Cotton Candy".

Frodo Baggins: Frodo Baggins is a fictional character in J. R. R. Tolkien's legendarium, and one of the main protagonists of "The Lord of the Rings".  Frodo is a hobbit of the Shire who inherits the One Ring from his cousin (referred to as his uncle) Bilbo Baggins and undertakes the quest to destroy it in the fires of Mount Doom.  He is also mentioned in Tolkien's posthumously published works, "The Silmarillion" and "Unfinished Tales".

Supporting paragraphs: Bilbo Baggins The Hobbit
Answer: 21 September 1937