What's to keep you from putting a little copper sulfate in your cleaning bath? It will spontaneously deposit a very thin layer of copper on the steel, protecting the surface. If the container is stainless steel it may be coated, too -- but I'm not sure about that. If that's an issue, test the container with a drop of copper sulfate solution on a noncritical place like the lip of the container.
I should have said, "in the absence of anything else it will deposit copper". If you've got soap in the cleaning bath the CuSO4 probably will form a copper soap compound ("soap scum") and drop out of solution. Baths that use alcohol or acetone would be all right. I'd guess that a nonionic surfactant like SC80 or Tween would be compatible, but would test before using it on something I care about.