I use a product called "Iron Out"

You can find it in stores where watersoftener supplies are sold.

I do not know its chemical makup. But it will eat up iron oxide (rust).

Get some and dilute it with water and either soak or apply generously with a cloth. You will see how nice that stuff works but the bluing will still have been eaten away by the previous rust. In general, you will find other uses for Iron Out around the house.
I add some to the water softener to clean the rust from the beads as it is much cheaper than buying the salt with rust removing addatives.