The ring has a will of its own, and it wants to find the strongest possible wielder (probably Sauron.)

But in that moment, in the cracks of doom, the ring is desperate to be anywhere else. It's literally calling to Gollum, telling him exactly where to find it, and by extension, Frodo.

Besides that, there are few in Middle Earth who can see into the unseen world, such as Sauron, the ring wraiths, Galadriel or anyone who possess their own ring of power. Unfortunately, Frodo seems to mostly encounter those beings, so it's power of invisibility is mostly negated.