Much of the music in colonial America was transported from places like England, Ireland, and Scotland.. Dance music played an especially important role in social events in colonial America and John Playford's The Dancing Master, first published in 1651 included a lot of dance music. This music also included quite a bit of improvisation; a tradition that undoubtedly was carried over from places like Ireland and Scotland where the tradition of fiddling went back centuries.
Hesperus' 1997 album Early American Roots captures the essence of what early American music might have sounded like.