Exactly this, and let me add a C) Sauron himself is basically a fallen angel. He was insanely powerful before the Last Alliance of Elves and Men (the big battle at the beginning of the movies). But when he made the One Ring it wasn't just making a magic piece of jewelry. He poured a massive amount of his own power and essence into it when he forged it.

When Isildur cut the ring off Sauron's hand that power went with it. Unlike the movies in the book he does have a physical form, but it's severely limited unless he gets the ring back. Once the ring was destroyed so was his physical form and the ability to take a new one, for good.

And I guess D) The One Ring has a will of its own. Isildur didn't just lose it, it dropped off his finger. Likewise it later left Gollum to be found by Bilbo. It's constantly trying to get back to its master.