Because Sauron still existed as a weakend ghost after the destruction of the ring, I like to think that Frodo found him and followed him around, telling him all the times that the ring was close to him and he didn’t know.
“Bilbo wore it in Mirkwood, that was pretty close to Dol Guldur. I was across the river from the Witch King, I guess you knew that. But I was also across the field from him as he left Minas Morgul, and I was right next to the Black Gate. So many times you could have gotten it back! Also I walked across Mordor, that must really bother you. Hey where are you going?”