Wood stock or sythetic? Your bore cleaner isn't stinking from the barrel; the dry patches should have gotten that out. It's in amongst the nooks and crannies between the parts. First, if you can re-check your zero afterwards, take the action out of the stock and wipe the stock under it down with a cloth or gauze wet with alcohol, to wipe it off. Make sure it's dry. Then wipe the underside of the action, but re-wipe with a lightly oiled cloth therafter, too. Take out the bolt. Degrease, lightly oil, re-insert. Magazine springs can sometimes collect bore cleaner. Degrease, lightly oil, re-install. Sling: VERY difficult; it's porous. Good excuse to get another one!
Wood stocks you might take and wipe down with a rapidly evaporating substance to remove the bore cleaner, but I won't be held responsible if it hurts the glossy finish of your pride and joy! My rifles are shooters only, not for looking at!
Good luck.