Fully developed color film contains no silver. Bleach in the process converts developed silver into soluble silver that is then removed by the fixer. What remains in the film is cyan, magenta, and yellow dyes. These create all color and density you see. Applying a bleach for the dyes to film post processing will result in fading of the image, not desaturation. Greys in color film are a result of equal amounts of the three colored dyes. This is called a chromagenic grey.
If you desire a neutral grey, this would be an additive process not a subtractive one. proper amounts of retouching dyes, painstakingly applied to the film to shift colors towards grey. So if an area of the film is red, cyan would need to be added to that area to bring the color to neutral grey. Because it's additive, it would also increase density in the area.
Such a feat on camera film would be incredibly difficult. When we used to retouch on film, a large format inter-positive would be made. Essentially an 8x10 11x14 or 16x20 "slide". The larger format would make retouching possible.
A more feasible direction would be to shoot the image in black and white then hand tint the areas to add color, much in the way old black and white prints would be colored by hand. This could be done directly on film using retouching dyes - if you can find them, or on black and white prints using Marshall Photo Oils and Marshall Pencils that are specifically made for the purpose.