Hi Marauder,
Here is what I do, with NO rust ever. When I get home from the range, I put a large tea kettle filled with water on the stove while I strip the rifle down. (I worry about water trapped in between the stock and metal.) With the rifle stripped down, I hold the tang and pour HOT water through the bore and rinse the bolt. I do this off the deck so I balance the rifle on the railing and the water goes on the ground. Next, I use a cleaning rod and brush with dish detergent to scrub the bore, from the breech if possible, then rinsing again with HOT water. Note the metal will be HOT, use an oven mitt. While the rifle drains leaning against the deck rail, I thoroughly, rinse the cleaning rod so as not to transfer any salts back to the rifle. I actually also have two 30 cal. rods and keep one strictly for non corrosive and post washed bores. After I rinse the cleaning rod, I clean the rifle as usual with #9 followed by some Kroil. The rifles are stored in a safe with a Golden Rod to keep the air dry. The rust you see may be a result of water left in the bore from cleaning or condensate. The use of HOT water heats the metal and helps dry the rifle before I put it back together. I know from previous posts your rifle is among you prized possessions, take the time to clean it properly. Probably, the best trick is to clean as normal after rinsing, as this will help get rid of any remaining moisture. HTH
Best,
Rob