Removing Fabric Dye That Transferred in Wash?

I have a lovely pale teal/seafoam colored dress with white lace at the top, it was accidentally thrown in with a brand new black article of clothing and some of the dye leeched into the dress. The problem is, after it was washed it was thrown in a drawer and stored all winter, so the stain has been setting for several months.

I tried using a stain removing spray, letting it soak before washing in hot water, but the stains only faded a few shades, and I am afraid they are permanently set. I am hesitant to use bleach, even diluted, for fear of ruining the dress entirely (if it is even salvageable at this point) This is a real shame because the dress is so pretty and perfect for the hot summer days.

By Haley C