In the shots of "Hukana Mattata", Simba is shown aging, but Timon and Pumba don't appear to have any changes due to age. Thus, it seems that it could only have been a few years (like 2-3).
On the flipside, it seems hard to believe that Scar's mismanagement of the Pridelands could have gotten things to be as dire as they were in only that short amount of time.