Well, that's the thing -the semantics of English allow different people to mean totally different things by "musician." For some, that implies a person with a deep vocation in music, whose identity is defined by their capacity to make music (a very high bar, by which few bass players are true musicians). For others, it just means anyone who picks up an instrument and plays a note (a very low bar, by which all bass players are a subset of the category "musician" by definition).
I think what the OP is really asking, though, is how we see the role of the bass in our musical lives - do we think of ourselves fundamentally making music and the choice of bass as an instrument to do it on is incidental, or do we have a special relationship with the bass guitar and that's the lens that we look at the rest of music through?
Myself, I'm somewhere in between. I used to play saxophone in school, took some rounds of piano lessons, took up mandolin for singing around a campfire, play some guitar in church and when writing songs, etc. So I guess that makes me a "musician" in that I don't exclusively play bass. But I dropped sax in 10th grade to focus on drama club and never really thought of myself as a "musician" in the vocation sense banging out campfire songs on mandolin. It was bass that really made music "home" for me, got me into bands and performing in front of audiences and all that.
