I believe the pre-Scruggs Monroe band music was probably just called Country Music. In the early days of Bluegrass it was stilled included in the Country genre. I think early country music is what many of us consider the real Country Music. Stringbean was the previous banjo player who played the clawhammer style. I think of this period of Monroe as closer to stringband or even old timey music.
I think Bluegrass music is more recognizable when it includes banjo but I believe Bluegrass is not just the instruments but the style or approach to the way the music is presented.
Cabin Fever String Band, National Pike Pickers