And I have removed the visible rust on the right side of barrel and I'm still working on what I can remove with respect to the residual pitting.
One of the items that rusted was the chrome steel ball on the bolt and a small exposed area on the body of the bolt. Initially, a combination of oil and 0000 steel wool took care of the rust but left the area where the chrome steel had rusted blackened and not shiny. The bolt body area still has its satin finish with a slight visible blemish where the rust was.
For the ball on the bolt handle and other reflective (shiny) sections of the bolt handle affected by the rusting, I have used Autosol metal polish with 0000 steel wool to polish and largely restore the reflective nature of the bolt handle and bolt ball.
However, I am hesitant to do anything with the small area on the bolt body. Now that the rust has been removed and I've stopped the rusting, I may just leave it alone. But I am open to suggestions. The area affected is only about the size of a No. 2 pencil eraser.
Added photos:

Underside of bolt handle ball after rust removal and application of polishing compound. The shine on the top is restored but pitting is evident where the rust was more prevalent.

Residual "stain" after removal of small amount of rust on the chrome steel bolt. Looks like a "running man". I'm hesitant to do very much on this part of the bolt