I agree 100% about the mindset.
I just look like a guitarist holding a bass.
Man, it takes some time. The most important thing is the awareness and as you say the mindset. Recognizing that an electrical bass is not just a guitar with less strings
But indeed there are people out there who can do both in a great way. My standard example is Sting who is a reasonably good guitar player but an incredible (band oriented and tasteful) bass player. Can't get enough of watching him playing the bass...
Personally I am a guitar player and though I like to grab my bass and do some basic tracking for demos and recordings I would never claim to be a bass player. Missing so much of the background and skills needed. Nevertheless it helps me a lot to push creative processes and sketch things which the "real bass player" in my band can enhance and adjust to be the real thing in the end.