I choose to take a more holistic approach to things. The idea that you need to be 'one musician' here and 'another musician' there only adds complexity to what is a very simple thing - being a musician.
While I understand the idea that "people pay to be entertained" - and agree with it in spirit, it's the question "what is it that people respond to" that needs to be addressed. Superficially and disregarding all else, it can appear to be the fact that the people on stage are jumping around and being physically exciting. But if that's all it took, you could put any idiot on stage and as long as he jumped around a lot, people would be entertained - and we know that's simply not true.
OK - What if a technically proficient band took the stage and just sat on chairs and played the most technically correct show, musically, but did so entirely motionless. After a while, people would stop watching them. There would be nothing to see and they might as well be listening to a recording.
To simplify the whole thing, as a musician, you need to practice your craft regularly and become proficient, technically and musically. Part of that includes experiencing your craft emotionally - the art of it. If the music is not impacting you emotionally, how can you expect it to impact the listener/watcher?
So that means along with keeping your technical and musical chops honed, you need to transcend the mechanics of playing music and experience the music on an emotional level as well. If you are doing all of that, you will end up reflecting that in your demeanor when you perform.
If you are genuinely enjoying and experiencing your art and craft when you perform, people will respond to the vibe you put out - the energy you transmit. Sounds like hokum, but it's true. Animals detect your energy - so do people. If you put out energy that's wishy-washy, scared, shy, any version that says, "I'd prefer you not look at me" - that's what people will pick up on - even if you are playing really well.
ON the flip side - if you haven't practiced your craft and feel you need to supplement your inadequacy by faking it - putting on a false representation of energy - people will pick up on that too. Now you could put more energy into faking it and become a great actor and successfully pull of an energetic display based on your refined acting skills, but I'd argue that's not the goal of most of us here as bass players.
In a live show, moving is a good way to engage the audience, superficially. Moving in a way that honestly projects the energy you feel when you play will engage them on a deeper level.
People want to see people on stage having the best time and who are genuinely into what they're doing. People live vicariously through performers and the more honest and genuine the performer, the better the experience becomes.
So the "secret" is no secret at all. Hard work in the woodshed toward the honest goal of being the best musician you can be will result in you being very confident on stage. Being confident on stage will allow you to enjoy the experience of being on stage to it's fullest. You enjoying the experience of being on stage to it's fullest and playing well and with confidence will translate into a great energy exchange between you and your audience. Your confidence and demonstration of how you experience your music will inspire people to respond to your energy. Their energy will, in turn, inspire and energize you.
That's the goal.
How you move will be determined in the moment and by that energy exchange. So you should optimize your ability to experience the thrill and enjoyment of playing in front of an audience in order to maximize your ability to participate in that energy exchange.