hello pal.
applying gun oil will not remove rust,is more of a pervention than a cure. i would look at where your storing the gun, rifles are rust magnets if not looked after.
if you have some light serface rust,take some tin foil screw it up and with a very small amount of oil(drop or two) rub it down the action of the gun, this will remove the rust but not scratch the blueing of the action. good wipe and clean down after and will look lots better.
when you have been out remove the stock and alowe the gun to warm up/dry out nateraly,when dry take you gun oil and cloth and rub the r