best way to clean a medium dirty spot from white cotton cloth?

Well, it helps to know what the stain is. You've tried the usual bleaching solutions but what is the stain made of? You need to break up the stain's materials in order to have a chance.

For protein-based stains, you need an enzymatic cleaner. General color stains want bleach, but that didn't work. Some color stains can be attacked with solvent-based cleaners, and I think for best results you might want to take the item to a professional cleaner if the garment is that important to you.

Sometimes you can't really do anything, like with a red clay stain. You're done, the material is now dyed and there's really nothing you can do. At some point you just have to give up.