The drive pulley being loose on the splines does sound like it is coming from the transgression (it is). Check your nut and pulley washer for any signs of pulley motion, and
grab that pulley and see if it moves on the splines.
A loose pulley nut is a common enough problem on this bike, after all.
Taking your bike to a Suzuki dealership is a BAD idea -- yes they will find all sorts of expensive problems for you with your transmission, and your clutch system, and various bearings -- none of which are real or actually apply to your problem.
Your wallet will certainly be lighter though. Next thought, hmmm (how to say this in the best fashion ???).
If you came here looking for some dealer service trip pre-information with no intention of actually taking a simple belt cover off your bike and shaking a drive pulley to see if the nut is loose, then you got whatever "good information" you came to get.
Here's some more good information if you want to get your hands dirty .....
(put this up into your browser's search bar or just double click on it)
http://suzukisavage.com/cgi-bin/YaBB.pl?num=1335739552/15