As long as it is not IN the bottle. If it was, the ring would be drunk with power.
There are quite a few “almost accidents” in Tolkien’s mythology. The world seems to arrange itself to realize the desires of the agents of Good, while Evil often has to bludgeon out the means for its ends.
Well, there’s nothing in the books to say this didn’t happen - but there is no indication that it did, either.
Even while Bilbo wasn’t wearing it, he was still subject to the Ring’s power-- That’s the whole point of why it was hard to give up. And the One’s power trumps the Threes’ power.
Bah, I give up. So The One could beat Narya if ensconced in the root cellar next to the 'taters, being wielded by nobody? I can guess your answer, but this strikes me as ridiculous. Frodo couldn’t wield the ring (cf Galadriel’s words at the Mirror), nor could Bilbo. Apparently the ring wields itself in your scenario. If Sauron needed to wear the ring to use its power, why doesn’t Bilbo?
Was Frodo wearing the ring when he refused to destroy it? No, he only put it on after making that declaration. Wielding the ring means using it for something, and, per your analysis, must not include making yourself invisible. But I think merely having put the ring on gives it a level of power over you, even if you take it off. And if it has power over you, do you not think you could wield it from a distance?
I am unaware if Smeagol had ever put on the ring before he killed his friend, though. If not, then the ring clearly can woo people without even being “wielded.” All they have to do is be near it. Think of it as like the headlights on your car to deer. They have an impulse to follow it, even though it is dangerous.
Did it not tempt Galadriel even though she wasn’t wearing it?
Well Frodo tried giving the thing away to just about everyone but Boromir. He asked Gandalf, Elrond, Aragorn and Galadriel.
Not enough is known about Smeagol I think. The ring might have willed him to kill his friend but, then again, he could have just been a bad guy.
And also, Bilbo stole the ring and lied about it. Whether that was to assure the rest of the dwarves that he was a thief or to protect the ring, again, I’m not sure. But I always figured the ring had a lot to do with it. The ring had Bilbo find it, made him cheat in the game then made him lie about it to his friends.
But what about Boromir? Was he just stupid and greedy or did the ring figure he was the most susceptible and spent all of it’s power trying to influence him.
Boromir wasn’t either stupid or greedy, but he desired power and its exercise. That’s why he was so vulnerable to the Ring.
It seems to me that in Tolkien’s world, magic tends to be a subtle thing, and the greater the magic, the more subtle it is. The only overt example of magic Galadriel has is her Mirror, for example, and we never see any overt magic from Elrond at all, despite his ring being the mightiest of the Three. Gandalf’s visible magic seems to have been limited to things associated with fire. Saruman goes for influence (via his Voice) and technology.
Here is an FAQ about the Ring. Way down the page, there is discussion of the sentience of the Ring. Although it does not discuss my theory of the Ring’s malice leading to its own destruction, it does cite this passage from the books:
Accidents are often not accidents in Tolkien’s world. The Ring slips from Isildur’s finger; it slips from Gollum’s possession. These are the will of the Ring. The Ring even slips from Bilbo’s finger briefly, shortly after he finds it, so that he is almost captured by goblins. It seems to like to betray its bearer, so long as that bearer is not Sauron himself. Given that Frodo so precisely threatens Gollum with his eventual fate, and does so enabled with the power of the Ring, I think it is quite reasonable to believe that the Ring itself betrayed Gollum into his fatal ‘accident.’
The Ring did not need to be worn to grant power to its bearer. Sauron drew on its power continually. It is postulated in the FAQ that the Nazgul’s Rings were actually in the keeping of Sauron, but they certainly drew power from them. Both Gollum and Bilbo continued to survive with little aging after losing possession of the Ring. Obviously, the power the Ring grants was greater when the Ring was being worn than when it was off, but equally obviously the Ring extended some power to its current bearer even if it was not being worn.
I think in that passage it is the Ring threatening Smeagol, not Frodo. The voice comes from the wheel of fire at Frodo’s breast, which is where he keeps the Ring. I always thought that was the evil of the Ring betraying itself - it lays a very specific curse on Smeagol - “you shall be cast yourself into the Fire of Doom” - and it backfires badly when the curse comes true.
In The Silmarillion, Tolkien wrote that the bearers of the Three Rings took them off when they perceived that Sauron had put on the One Ring, so that he could not control them. I always thought that they (or their successors, such as Gandalf) didn’t actually put them back on their fingers until after the fall of Barad-dur, by which point the Three were essentially powerless anyway.

In The Silmarillion, Tolkien wrote that the bearers of the Three Rings took them off when they perceived that Sauron had put on the One Ring, so that he could not control them. I always thought that they (or their successors, such as Gandalf) didn’t actually put them back on their fingers until after the fall of Barad-dur, by which point the Three were essentially powerless anyway.
No, once the Ring was cut from his finger, the three were put back into use. Indeed, Frodo actually saw the Ring on Galadriel’s finger at her Mirror. Elrond, Galadriel and Gandalf wore and used the Three.

I think in that passage it is the Ring threatening Smeagol, not Frodo. The voice comes from the wheel of fire at Frodo’s breast, which is where he keeps the Ring. I always thought that was the evil of the Ring betraying itself - it lays a very specific curse on Smeagol - “you shall be cast yourself into the Fire of Doom” - and it backfires badly when the curse comes true.
The FAQ I cited above goes into the possibility that it was the Ring rather than Frodo speaking, and ultimately rejects it. But your last sentence sums up my position rather well, except that the idea of casting yourself into the Fire of Doom came from Frodo. But the Ring seized on the opportunity to betray Gollum.
I liken it to the idea of true evil presented in the story. Sauron is the main villain, and is presented as the ultimate evil, a super powerful being of pure malice. But we never actually see him and none of the characters ever interact with him.
It’s the second idea of evil, the more subtler kind, that the heroes have to fight against. Greed, thievery, arrogance, deceit, those are the true evil, all represented by ring. In the end though, such evil traits are ultimately self-destructive. The ring is able to thrive for a long time on emboldening the evil within anyone who holds it, but when it started the fight between Frodo and Gollum at the crack of doom, its evil tendencies finally led to its demise.
Evil is fundamentally stupid, because it’s short-sighted. At least, that’s what I take away from it.