But Saruman assumed that the reason Sauron was set up in Dol Guldur was that the Ring had been lost in the Gladden (much nearer to Dol Guldur than to Mordor). This may have been Sauron's assumption too, although he also may've had an inkling of Gollum's location.
So driving Sauron and presumably his agents out of Dol Guldur meant driving them from the Ring.
