Sort of a loaded question, but Ill take a stab at it.
Well I guess for me, I always considered myself a "Bass-Player". Sure I can play a song, pretty good quite often. but for the longest time I didnt really even know the fret board, (E string 3rd fret, then A string 7th fret kinda stuff; not 'G' up to 'E') yet I could play the hell outta (___name_that__) song. Plus, I knew a few handy techniques, (not afraid to grab a pick) I had decent ear, had pretty good sense of time and rhythm..
So to shorten a long story;
I kinda reserved the term "Bassist" for those that know enough theory to apply to the Bass and also can convey those musical ideas such as rhythm, harmony, melody; Guys/Gals who know chords (in all keys, or know how to figure them out quickly) and know about quality of chord tones...Those whom can solo when called apon, know about "Tension/Resolution" and the like. Those who can CREATE music, not just cop it. to me that is a Bassist.
so even tough I dont have all my theroy knowledge down, (will I ever?, seems like the tunnel never ends..) after many years -of sometimes failing; and sometimes fronting.- I am most recently considering myself a true Bassist.
though its kinda an eye of the beholder deal in a lot of aspects.
I can sing, but Im not a singer.
I can play drums, but I am not a drummer..
I can play a Bass, but now, yeah.. I do consider myself a bassist ('cept for maybe them solo's.. still working on that aspect lol

)