This rifle has many details of the Lexington School of riflemaking in Kentucky. Those details include the guard with heavy front post, triggers with large tab on the front "hair" trigger and rather straight back edge on the rear "set" trigger, use of four ramrod pipes, small raised ridge on end of butt plate return, straight comb and toe lines, etc. It also has the "scooped" cheekpiece and flattened top of comb found on many Lexington rifles where the maker had NC roots.
The Lexington School covers the Bluegrass counties of Fayette, Scott, Franklin, Jessamine, Woodford, Clark, Montgomery, and Bourbon. However, your rifle also lacks a few important details of a Lexington School rifle, including the school's distinctive "wavy line" molding line terminations, particularly under the cheekpiece, also at rear pipe and lower butt toe molding where it ends under the back of the guard's bow.
This rifle, in my opinion, is a good example of a "Secondary Lexington Rifle." Those rifles were made either near the Lexington School, or in fringe areas of the Lexington School, and Bath County fits into that description, being on the northeast corner of the Lexington School's known counties.
I have a rather similar rifle, same guard, triggers, stocking, four ramrod pipes, scooped cheek and flattened top pf comb, etc., but lacking some Lexington School details, possibly made by the maker of your rifle or someone close by, but heavier barrel and smaller lock bolt washer. My rifle is also unsigned, despite having a relatively clean barrel surface where a name or initials would be easy to see. I thought my rifle, based on its description, probably came from a county on the northern edge of the Lexington School... and Bath County is pretty close to that guess. The two volume set of books, "Kentucky Gunmakers 1775-1900," covers the Lexington School with many illustrations, and describes and illustrates examples of the secondary Lexington rifles. It is advertised on this site, in case you migh have an interest in it. Shelby Gallien