Why didn't Bilbo see everything bluury-like?

[Manwe Sulimo]

Remember, when The Hobbit was written, the Ring was just a "plain old ordinary magic ring", not the One Ruling Ring of Sauron.

If you want to look at it from a plot standpoint, Sauron wasn't at full power, and had not yet been lusting after the Ring in all his spare time. Also, the movie (in that sense) is innacurate: it didn't become "blurry", except near Mordor:

At once [Sam] was aware that hearing was sharpened while sight was dimmed, but otherwise than in Shelob's lair. All things about him now were not dark but vague; while he himself was there in a grey hazy world, alone, like a small black solid rock, and the Ring, weighing down his hand, was like an orb of hot gold. He did not feel invisible at all, but horribly and uniquely visible; and he knew that somewhere an Eye was searching for him.

In the Prancing Pony, Frodo suffered none of these side effects.