Of course, you know that bluing is also applied in coats while also polishing between each one?
I'm not sure where you got that info.
In the case of hot caustic bluing, the metal is polished, degreased, then immersed in a boiling saturated KOH solution. When it comes out, it is done. No more polishing.
Then there is rust bluing, where the metal is polished, degreased, then rusted with a mild acid solution, then boiled in distilled water to convert the rust. When the part is removed from the water, the loose rust is carded off, and the process repeated. But the metal is only polished onece.
Even in nitre bluing, the metal is first polished, then immersed in a boiling saturated metal salt solution, when it is removed it is done.