I intentionally work at trying to imitate the "feel" of whoever did the bass line for whatever cover song I'm playing, even if I'm improvising on the actual notes.
My early influences were Jack Bruce and Geezer Butler, and to a lesser extent, John Entwhistle, and then Chris Squire and Geddy Lee entered the picture and changed everything.
After my last band broke up violently (guitarist and drummer rolling on the floor, pounding each other) in the late '80s, I quit playing for over 35 years. After semi-retiring to a part-time job and finding myself with "too much time on my hands", I decided to pull one of the old basses out of the attic and relearn. Quickly realizing that I no longer had any idea how to play the damned thing, I decided to "reinvent" my playing style, actively seeking other influences such as Flea, Justin Chancellor, and other grunge and new-metal players. Three years later, I'm finally able to pull that stuff off reasonably well, and am starting to play out again with a mostly grunge-era cover band with a couple of younger jazz players learning rock.
I recall hearing one local guitarist throw in some convoluted licks during a solo on some otherwise boring cover tune, and felt certain that I recognized the influence. "Was that a bit of Frank Zappa in that last solo?" "No, Adrian Belew." Turns out, Adrian Belew got his first major professional gig with Frank Zappa, before joining King Crimson. I recognized the influence of the teacher of the player who influenced the local guitarist. We're always influenced by what we listen to, whether it comes out audibly in our playing or not.