I have died my hair BLACK and would like to bleach a section of hair at home...?

I've heard that dying already died black hair with a blonde dye can make it turn orange. If this is true i don't want to do that. Haha I would like to bleach out a small portion of my hair (about a 2 inch section in the back) So that i can dye it different colors. Is there any way to do this without going to a salon or buying a whole thing of dye just for that one strand? Thanks. :)