Would be inclined to agree with the post stating it's the banjo. Regardless of playing style the 'sound' of the banjo defines a band as being 'bluegrass' to most audience members. Unless, of course you play in a plectrum style then you're a 'Dixieland' band to most people. And if you're playing Texas as opposed to Urban swing the pulse of the music in more like straight country than say 'be bop'. As the other post suggests it doesn't matter what they call it as long as you get paid for playing what you love.