Can a bass player them self, really be their favorite bass player?
Here's my interpretation of your question:
In some ways yes, and in some ways no.
You can never be anyone but yourself, no matter how hard you tried to mimic/copy/pay tribute to someone else. That doesn't mean that it's wrong to try, provided you can do that but also take in other influences and grow as a musician.
In my lifetime, I've tried to "be" Sting, Paul McCartney, Jaco Pastorius and Mark King (Level 42), to name a few. I still do. I learned a lot by trying to do exactly what they do. You could say it provided much motivation to learn/play bass and has been incredibly significant in my development as a bass player, singer and musician in general. They were my teachers, and still inform my musicality, and spur me on to continue to be better. It has helped my playing, technique, ear training, attention to details, the bass playing/singing duality, etc...
Insofar as the trying to "be" someone else has these kinds of positive, beneficial effect on you, I'd say go for it. To heck with the naysayers. "Be" whoever you want to be. I think I'm going to go put the CD player on, and "be" Peter Cetera (of Chicago) for a while...
On the other hand, don't go to the point of trying to "be" someone else so much that you can't do anything else but "be" that artist you are trying to emulate. You gotta be able to keep open ears, listening to new stuff, adding influences, experimenting. I knew a guy back in high school who obsessed over Yingwie Malmsteen, and at a certain point where that was all the guy could talk about (and YJM initials all over the place), I was thinking (but never said), like: get over it dude- there are tons of great musicians out there besides just this single one. Some people obsess like that but you gotta have BALANCE and DIVERSITY. Even in my moments of "Jaco-fever" I was always listening to other things and working on original ideas or putting myself in situations where I had to come up with original ideas.
Lastly, while it's fine to "be" someone else as much as you can, also think about developing yourself in terms of original ideas- don't get yourself boxed in and in such a comfort zone that you can only conceive of doing that which is provided for you via recording and/or notation. Emulate Geddy Lee, and be the best damn tribute you can be (if he/Rush floats your boat, or whoever else...) but also join a jazz band or something with a highly interpretive/interactive component. Develop both sides equally as much as possible. This is the "coverband -vs- originals" argument (in disquise) which is very tired and played out. I'll give you the quick answer on that one- DO BOTH!
I humbly submit these opinions.
Best to you.
