I've had a long time to think about this, it happens to me all the time. I've been a bass player since 1963.
Another thing that I've noticed is no matter where I am or how long I've been there, towns, cities, countries or even shopping centers or grocery stores people always and easily approach me, often mistaking me for a local or somebody who works there, somebody who is approachable and knowledgeable. I am often told I look like a bass player, I don't try to, I look like a biker with knives visibly on my person, I carry a pistol everywhere I go, I ride a Harley, I don't cut my hair and rarely shave, but complete strangers are happy to see me. I don't scare anyone as rough as I look, I think I should but it's not the case, there is something deeper that people see.
I believe the vibe of which we speak is that no mater where we are we belong there, comfortable in who we are and self assured. The foundation of the band is what we are, we are not in it for the glory but use our power to make things right, to control the rhythm, catch the guitar player, remind the drummer where we are. not for glory rather to effectively bring it all together, to make a coherent piece, the blender, the bridge between the various parts of the whole.
This I believe is what people pick up on, we are comfortable in our own skins not wishing to be anything else and to bring form out of chaos.