The One Ring and invisibility

[The Might]

One thing that you must not forget here is that the Ring did have a will of its own. We see Gollum seeing a wheel of fire on Mount Doom and hears the Ring speak. So clearly it could and would use the bearer to fulfill its needs.

‘Begone, and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom.’

So the Ring could, depending on the need, exert a stronger or weaker force over the bearer. For example it might have tricked Bilbo into thinking it was a good thing so as to escape from the Misty Mountains, but later tried to slowly wear him down and make him a wraith.
Fortunately, he proved to be quite resilient.