Just where, when and how the Bean family gunsmithing style evolved is sort of a mystery. The Beans settled in East Tennessee early, by around 1767 and came from Virginia. Some have claimed that the first generation settler William Bean made rifles but to my knowledge there is nothing docuemented to show that. There are references to rifles being made in the region in the late 1700s but we don't know what they looked like.
There are signed Bean family guns from later generations (like Charles, Baxter, and I think a Joseph or Jonathan - 2nd quarter of 19th century), and there are references to some Bean gunsmiths (I think Russell Bean is the earliest referenced as a gunsmith - not sure (?)) that we don't have signed examples of their work. In Foxfire 5 they say there were suspected to be 5 generations of gunsmiths in the family.
Some early gunsmiths who moved into the region before 1800 were the Bulls and Joseph Bogle, and their early work shows similarity to guns being made in Southwestern Virginia moreso than what we think of as the classic late flint, "Bean" style east Tennesee gun. The Bull family guns evolved into their own distinctive styles with time. So perhaps the same is true of the Beans as well.
So the style of the mounts, and the architecture of the Bean style were there by about 1830, probably even by the 1820s. Earlier? We don't know. Did they develop the style or learn from someone else? Again, we don't know. Earl Lanning's Matthew Gillespie rifle shown in Dennis Glazener's book shows that the Gillespie style mounatin rifle was pretty much evolved by 1815 or so, so it is possible the basic Bean style was as well. Or, perhaps some of the guns attributed to southwestern Virgnia in the 1790-1820 era were actually made in Tennessee and looked very different from the later mountain rifles.
In any event, the east Tennessee style seems to have evolved and remained through being somewhat isolated - I think you can be safe in assuming it was there by at least 1830 and was used for the remainder of the 19th century.
Guy