The fire may have made them too weak to attack at that time. I think the WK thought that the hobbits were disorganized and he would easily be able to regroup with the other nazgul and then grab the ring. He prolly didn't think that frodo would be taken to rivendell where he couldn't enter.
The Witch-king could have entered Rivendell at any time, but chose not to. What all of you are missing is the character of the Witch-king. He is (or was) a man, a coward of a man seeking glory and power through unearthly means (the rings). That kind of character carries over into the ragged form seen in Lord of the Rings. The Witch-king is not "Sauron, but weaker." He is not without fear. All the Nazgul fear many things, such as fire and being seen by many eyes. Hence, they avoid fire and dare not enter cities except at the greatest of need.
TheJord is right. The Shire is a long ways away from Mordor and the Nazgul's overprotective mother. They have no allies, no sanctuary, and no way of calling for help if help is needed. The Nazgul had to be extra-cautious, using all the time they had available to them in order to get the job done. Plus, they had no idea that Hobbits were resistant to both the Ring's corruptive power and the evil instilled into their blades. As far as they knew, Hobbits were as susceptible to their power as any other being (if not more susceptible).
SoP brought up another good point. Tolkien made language a tangible object in Lord of the Rings. Words are weapons and defense. Frodo screaming '
O Elbereth! Gilthoniel!' in the Witch-king's face hurt all the Nazgul pretty bad. And then being confronted by the descendant of Elendil forced them off.
