Genealogy of Bluegrass- 22511: Bluegrass
Agrarian? Webster's: of or relating to or characteristic of farmers and their way of life.
Some were farmers, but others were wood harvesters, small town business employees, some worked in mills and stockyards. Southern, Rural and small town, I think, cover it better. Agrarian also has the aura of some of the farmers' political movements.
Bluegrass, by your emphasis on Monroe and Scruggs, pretty well puts emphasis on the more commercial aspects of the music as developed in Nashville. Too restrictive.