I think a lot of the old songs went to America with the early settlers , but there was a definate two way traffic in the eighteen hundreds - Little Brown Jug was an Americanisation of an older song , that was 'collected' in UK in the late eighteen hundreds and Re Exported back to USA ! The Minstrel show connection with the banjo in Ireland may be a reasonable assumption , though there were a lot of VERY good banjo builders in UK at the time , which indicates a fair amont of popularity any way !