Just had something similar happen to me. A few words of advice, that may or may not be appropriate to your situation.
When you "rebuild" the carb, get at least a kit that has the float needle and seat:
http://www.ebay.com/itm/95-12-SUZUKI-LS650-SAVAGE-NEW-K-L-CARBURETOR-REBUILD-...My problem was the seat.. specifically, the o-ring that seals that to the body of the carb.
Check the air filter and air box for gas. (I drained about a pint of gas out of my air box, and the air filter was soaked. )
After draining the gas polluted oil, tip the bike left and right, forward and back, as far as you can and keep draining as much as you can.
(My legs are still sore from doing LS650 weight lifting
)
Remove the spark plug, put a tad of oil in the cylinder. Can't hurt, might help if you had some wash down from gas in the cylinder.
New oil, new filter, and spin it with the starter without starting (just leave the plug out). Don't run that starter too long, but run it enough to get the new oil moving around.
Repeat the drain and bike shaking procedures. Refill with new oil again. The oil filter is probably OK.. I didn't change mine again.
Put it all back together.. and if luck is with you, nothing got hurt from the gas in the oil. I was lucky!!