Here's my pro gunsmith's method to remove rust, but protect the bluing that's left:
Materials needed:
Kroil or CLP Breakfree. (Kroil is preferred).
A scraper made from sheet brass or a brass cartridge case with the mouth smashed shut and filed into a chisel shape.
A brass "toothbrush".
Apply a dripping wet coat of Kroil to the rusty areas and allow to soak for at least 24 hours, longer if possible.
The Kroil or CLP will penetrate the rust and will soften and loosen it.
After soaking, apply more Kroil and use the brass scraper to scrape the heavier, crusty rust off.
Then use the brass "toothbrush" to vigorously scrub the rusty areas.
This will remove all the rust but won't further degrade the bluing that's left.
Once the rust of off, wipe dry, and apply a coat of CLP Breakfree.
The CLP will continue to "work" on any remaining rust, and will prevent new rust from forming.
Unlike steel wool, this won't thin or degrade the bluing.
You can usually ID a gun that has been steel wooled, there's usually a crater-like area around rusty spots.
This looks like a pit with a crater-like area of missing blue around it.
This is caused by the steel wool hitting the crusty rust like a car hitting a speed bump and causing the steel wool to "bounce" over the spot, thinning the blue around it.