It couldn't of been longer than a week.

From the time he fell over board

-The night in Besaid
-A night in Kilika
-A night at Rins
-They spent a night at Djose
-And lets say another night for when they were under Lake Macalania before they got sent off to the Sanubia Desert.

Unless I'm missing something in there

Edit: plus a night or two on the SS Liki and a night at the the inn when Yuna watched Lord Jyscals sphere