Another approach is to buy some Gunzilla. It's made from vegetable oils, and it slowly debonds rust from steel. I've taken a small vial of it and set a small rusty tool in it. After a week or two, all the rust is lying on the bottom of the vial. Another time, I wet the rust-pitted bore of a rifle with it and let it sit in a gun vice for six weeks (I was away on business) before running a clean patch through. All the rust, as well as hard carbon mixed with it, came out with the first patch. It was all on one side of that patch, indicating it had not only debonded the rust and carbon but it had all slid to the bottom side of the barrel. My borescope showed nothing was left but bare steel, albeit there were pits where the rust had previously been. In your shoes, since Gunzilla is a finish-safe gun cleaner, I would wet the gun with it, especially on the rusty places, and put it in a plastic bag to prevent drying for a couple of weeks, take it out, and gently wipe the rust off with a rag. Repeat as needed.
Regarding Bill's mention of cold blues, some of them actually seem to activate metal and cause rust. I once had a handful of those little plastic colored yard flags used by the utility companies to mark buried cables and pipes. the "pole" on the flag is a length of carbon steel music wire. I cleaned and degreased the wires and dipped each one in a different cold blue and cold blacking solutions, rinsed them off, wiped them, and let them sit out overhanging the edge of a box so they were exposed to air on all sides of the bluing. After a couple of weeks, they all had rust blooms on them except the two that had been colored by Oxpho-blue and Van's Gun Blue. They remained rust-free. The difference between those two is they are both phosphoric acid-based, while the others are nitric or hydrochloric acid-based. Phosphoric acid solutions phosphatize the surface slightly, so they give you a little bit of preservative effect. I wouldn't count on it without soaking the finished and dried work in water-displacing oil followed by regular gun oil. Oxpho blue is the darker of those two brands, IME. Neither is as dark as something like Brownells 44-40 blue, but it causes the after-rust problem if you don't take care to neutralize it and get the nitric acid traces truely gone.