Why didn't Saruman go to the Shire to take the Ring?

[Inziladun]

Originally Posted by Gordis

So, finally, before midsummer 3018, Saruman understands that the One is in the Shire, maybe in Gandalf's direct keeping, maybe in the keeping of one of the hobbits under Gandalf's supervision.

Saruman can't have believed Gandalf possessed the Ring himself. Saruman's considerable knowledge of the Rings of Power would have made it clear to him that if Gandalf or any of the Wise had the One they would not have been able to resist the temptation to use it.
Saruman obviously suspected the Shire had some special importance to Gandalf, but there is evidence that suspicion was all he had. Consider the conversation between Gandalf and Saruman and Orthanc.

I have many eyes in my service, and I believe you know where this precious thing now lies. Is it not so? Or why do the Nine ask for the Shire, and what is your business there?

FOTR p291
Saruman did not know the One was in the Shire, or surely he would have gone there to get it, just as he told the Nazgûl.

Originally Posted by Gordis

Saruman's next move is to invite Gandalf to Orthanc, using the unsuspecting Radagast. Why? Most likely Saruman hopes that Gandalf will come bringing the Ring with him. That's why he orders Radagast to tell Gandalf the news about the nazgul. Would the Grey wizard leave the Ring unprotected?

As evidenced by the previous quote, Saruman's purpose in luring Gandalf to Isengard was to attempt to persuade him to tell the Ring's location, if he knew it.
The first evidence that Saruman had definite knowledge of the One's whereabouts isn't seen until the attack on the Fellowship at Parth Galen. He had to have been aware of their departure from Rivendell with a number of hobbits, and that was likely the deciding factor that gave him surety.