I've had this happen twice on various NSRs. Both times it was because the needle which shuts off the fuel to the float bowl wasn't fully closing.

You'll need to disasemble the carb, remove the floats and needle. Then clean out the area where the needle seats with a cotton bud (Q Tip) dipped in brass cleaner (Brasso). Both times the seat had become a little corroded or covered with crap so wouldn't allow the needle to seat properly/shut off the fuel. Spent about 15mins on each one......worked a treat

It's a fairly simple operation, even for me , so good luck.