For the reasons in Blantyr's second quote.
Maybe Saruman never knew Gandalf had the Third Ring, or maybe he thought it inconsequential, as the Three were not made to help the Bearers control others.
Did Tolkien ever call Gandalf, Galadriel and Elrond Ringbearers? The first time I heard them referred to as such was in the BBC radio dramatisation - when Gandalf said "I too am a Ringbearer."
BTW, great first post, Radtech51!