Sometime prior to the 2260s, the "old Bonaventure", and all hands, vanished without a trace on her third voyage, in what was later determined to be the Delta Triangle. The ship encountered a time warp vortex and became trapped inside Elysia, a small alternate universe, a parallel time continuum, that periodically touched the prime universe in the Delta Triangle region. In Elysia, the Bonaventure remained adrift along with a large number of other ships unable to escape.
This Bonaventure was, in hindsight, intended to be a successor of the later conceived Bonaventure (C1-21), as confirmed by Doug Drexler, creator of a wall display where it was featured, seen in DS9: "The Nagus": "By the way, 'Bonaventure' was absolutely a nod to the animated show." 
The Bonaventure was described in the final draft of the episode's script as "a ship something like the Enterprise, but smaller, not as graceful and sleek – but clearly powerful."
According to the Star Trek Concordance, the Human woman seen in the Elysian Council was wearing what was "possibly an early Star Fleet [sic] uniform," but it is not indicated whether she is from the Bonaventure or another unseen or unmentioned Starfleet vessel.
Star Trek: Star Charts (p. 64) named the ship as SS Bonaventure and listed the year it was lost in the Delta Triangle, over two hundred light years away from Earth, as 2079. This date would be consistent with the fact that a Human female was a member of the Elysian Council where everyone was stated to be several centuries old. The Bonaventure's 23rd century design features are, however, somewhat inconsistent with the early 22nd century Earth starship design, as it was later depicted in Star Trek: Enterprise.
The undeveloped Star Trek: The First Adventure movie was to feature the first dilithium-powered warp test ships in the 23rd century, called the Bonaventure and Bonaventure II, using a new technology Montgomery Scott and George Kirk worked on.
While the Bonaventure may have been the first starship with warp drive, it was later established that the first warp-capable ship of any kind was the Phoenix, launched in 2063. The existence of the SS Valiant, launched in 2065, is often used to ascertain the launch of Bonaventure as occurring 2064; however, it was never stated that the Valiant was warp-capable. It is implied she was not, as the magnetic storm that carried her to her destruction specifically overwhelmed her impulse engines.
According to the now apocryphal reference book Star Trek Spaceflight Chronology , the UNSS Bonaventure was a warp 2.5 cruiser of the Cochrane-class, under the command of Captain Hadrian H. Huckleby (β). The ship was Earth's first warp drive ship and began Earth's warp drive era with a trip to Tau Ceti four years after the first successful demonstration of warp technology. The ship was unaccountably lost on her third mission, eight years later, on the voyage to Sirius. The UNSS Bonaventure was stated to have a maximum emergency velocity of warp 2.5, although engines experienced a slight power breakdown at that speed. The Bonaventure was also the first Earth ship to use alien technology such as the warp guidance system.
In the novel Federation, Zefram Cochrane's first warp ship that traveled to Alpha Centauri was called the Bonaventure, conceivably the C1-21 or a sister ship, and his later personal ship was called the Bonaventure II.
The 2006 Ships of the Line calendar depicted a vessel with the registry number NCC-1000 that was reprinted and identified in the Ships of the Line art book derivative, released the same year, as a Bonaventure-class (β) vessel. It was designed and constructed as a CGI model by Aristomenis Tsirbas, who was requested by Mike Okuda to have his design become the class lead ship USS Bonaventure NCC-1000 (β), as a nod to the Animated Series vessel, when the book was prepared for release. (Star Trek: The Official Starships Collection, Bonus Issue 12, p. 8) As such, the ship received in 2019 its own outing in the British partwork publication Star Trek: The Official Starships Collection.
According to the ebook Where Time Stands Still, the USS Bonaventure was the first vessel equipped with the second generation of Cochrane's warp drive.