I'm sure Jason will be able to provide you with much more info on the subject (I'm not really into weapon systems
so old), but until the cavalry arrives...
In a word, so to speak

, John Spangler of
"Antique and Collectable Firearms and Militaria Headquarters" had the following to say on the subject :
Quote
Among most gun collectors, or at least Western history buffs, the term "Buntline Special" is considered to be a cowboy revolver with an extra long barrel. The popular myth, based on "Wyatt Earp, Frontier Marshal" by Stuart Lake claims that five of these revolvers were personally presented to famous Dodge City lawmen by Ned Buntline. (Wyatt Earp, Bat Masterson, Bill Tilghman, Neal Brown and Charlie Bassett were the purported recipients). Ned Buntline was the pen name of a popular author of the mid-1870s who wrote what we would call "action-thriller" stories. Buntline was very impressed with himself, and worked hard to make sure others shared an equally high opinion of him (sort of like our outgoing President). As is often the case with such people, the facts do not stand up when closely examined, and a lot of other statements from Lake's book are considered inaccurate.
In any case, about 30 of these guns were made by Colt in late 1876, shortly after the Custer Massacre but that is only a date reference, not a suggestion that there was a cause and effect relationship. The pistols are in the serial number range 28800-28830, with many variations in details. In general, they had long barrels (ten, twelve, or sixteen inches compared to the standard length of 4 3/4" to 7 1/2") a flat top on the frame with a flip up rear sight, and a detachable nickel plated bronze shoulder stock. Nearly all were made in .45 Colt caliber. One of these is on display in the Colt Collection at the Connecticut State Library in Hartford, Connecticut. Most of the others are in private collections, but a few have not been located.
With the increased interest in "cowboy" guns fueled by the popularity of television Westerns, Colt added the "Buntline Special" model to its offerings in 1958 with a 12 inch barrel. They made a Wyatt Earp commemorative with a 16 inch barrel came out in 1970 complete with a reproduction of the shoulder stock. Colt also offered extra long "Buntline" barrels on their .22 caliber versions of the Single Action Army starting about 1960. The "Buntline" story seems to have been spread by Colt about this time to help sales. Most of this information comes from R.L. Wilson's "Book of Colt Firearms."
It might be interesting to track down one of the old books by Ned Buntline and read it together to see what sort of books were popular 125 years ago. Your library probably does NOT have any, but most libraries can get nearly any book ever printed on "interlibrary loan" for you and it only costs a few dollars.
You might also enjoy seeing if you can find out if there is any "Cowboy Action Shooting" taking place in your area. There you could see men and women, and young people safely using all sorts of old style guns, maybe even a long barrel Buntline Special. They usually dress up in old west costumes and have funny names, and have a LOT of fun. They might even allow guests to try out one of their guns (with supervision, of course). The Single Action Shooting Society sponsors this sort of shooting sport and it is extremely popular all over the country.
For a more historical perspective on Buntline Specials have a lookie at
"Wyatt Earp and the 'Buntline Special' Myth". It's a pretty lengthy write-up, but if you make it through you'll get some idea about what was's so "special" about Buntline, even with some thechnical aspects thrown in for a good measure.