A few passes with a brush, a few with patches and done. Bringing windex to the range? Boiling water at home? It takes me 5 min at home with some Hopes or CLP, whichever is closer at the time. I've not ever had a single problem with my rifles. I've used this method to clean after shooting corrosive ammo in my rifles.
Finish by running a oily patch through the chamber and bore. If you need to deal with copper fouling, follow with something like Shooters Choice and a phosphor-bronze bore brush. It will get the barrel and chamber so hot that when you are finished, the heat will completely dry the metal. The scalding hot water will completely eliminate any possible corrosive residue in the barrel. The patch will get wet and form and effective piston. Place the muzzle in the hot water and "pump" it up the barrel. Put a cleaning patch on a jag and run it down the barrel to the muzzle.
When it is boiling, put the pot of water on the floor. Put a squirt of dishwashing liquid in the water.
Upon arriving home, put a pot of water on the stove to boil. If you can do so at the range, put a few drops of Windex on a patch and wipe out the barrel. Corrosive or non-corrosive is just not a big deal. It may be that the ammo you have is corrosive. It may be that the ammo you have is not corrosive. I have shot a lot of Mauser rifles, chambered in all sorts of calibers.