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

[Gordis]

Let us look at Saruman's actions and motives in summer 3018 closer.
What has really happened between the three Istari (Saruman, Radagast and Gandalf)?

Gandalf had been fond of hobbits ever since the Long winter (2758-60), long before Bilbo has found the Ring. He didn't hide his interest from Saruman and

Seeing then that Gandalf thought the Shire worth visiting, Saruman himself visited it, but disguised and in the utmost secrecy, until he had explored and noted all its ways and lands, and thought then he had learned all that there was to know of it. And even when it seemed to him no longer wise nor profitable to go thither, he still had spies and servants that went in or kept an eye upon its borders. For he was still suspicious. He was himself so far fallen that he believed all others of the Council had each their deep and far-reaching policies for their own enhancement, to which all that they did must in some way refer. "Concerning Gandalf, Saruman and the Shire" UT

So, in summer 3018 the One Ring is hidden in the Shire. Saruman doesn't know it is there, but is very much aware of Gandalf's interest in this land.

Then Saruman suddenly learns that the nazgul - all nine - have crossed the Anduin and are searching for "the Shire". How did he learn it? Most likely from Radagast - because how otherwise the Brown Wizard, who always stayed as far as possible from politics, got involved in this story? Radagast must have learned from his birds and beasts that his neighbours, the two nazgul of Dol Guldur, set forth, crossed the river, met the other seven and rode north together, asking questions. Radagast did what was his duty: he immediately went to inform Saruman - the head of his order.

Here Saruman most likely put all the loose ends together: Gandalf is interested in the Shire and goes there a lot, the nazgul try to find the Shire, and there is hardly any other errand than the search for the One Ring that would make Sauron send all the Nine to wander across western lands. The last bit can be proven by Saruman's words to the Morgul-Lord:

"It is not a land that you look for," he said. "I know what you seek, though you do not name it."- UT

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'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?

But that was not what happened. Gandalf came alone without the Ring. And here Saruman's actions do not make much sense, IMO. He took Gandalf out of the picture, imprisoning him in Orthanc. But he did nothing about the Ring. Why didn't he ride like the wind to the Shire himself, to get there before the nazgul?

And if I knew where this thing was hid, I should not be here, but long gone before you to take it.

- says Saruman to the nazgul in UT. But he lied. He DID know! Well, maybe he didn't know the name of "Baggins" (likely the nazgul only asked about "the Shire" at first, and started asking about "Baggins" only beyond Sarn Ford), but still, he could have found Bag End easily - as it was the place that his colleague Gandalf was known to visit. A couple of questions, a small amount of charm and persuasion and he would be led to Frodo.
The rangers at the border would have let him pass - wasn't he the head of the White Council? Frodo would have had no suspicions of him - didn't Gandalf speak highly of Saruman? He could have taken the Ring there and then, or carried Frodo to Orthanc - if he had daring enough.

But it seems Saruman hadn't got enough guts for it. He did the silliest thing - removed Gandalf and left the Ring completely unprotected for the nazgul to take. Or, considering that Gandalf had means to transmit the news of danger to the Ringbearer, prior to going to Orthanc, he left the Ringbearer enough time to make his way to Rivendell, where the Ring would be beyond Saruman's grasp.

What was it? Miscalculation? Cowardice?
What do you think?