Mix one part vinegar and one part baking soda in a small container to form a paste. Add more baking soda if the consistency is too runny and add more vinegar if the mixture is too dry.
Apply the paste with a scrubbing pad or nylon brush on the hair dye stain and allow the paste to sit for 15 to 20 minutes. Wipe the stain clean with a damp cloth.
Spray the stain with one or two squirts of hair spray to loosen up the hair dye.
Scrub the stain with a steel wool cleaning pad if the dye still exists. Use carefully to avoid scrubbing the finish from the wood floor.
Use a dry cloth to wipe the soap and hair spray from the flooring and follow up with a damp cloth. Repeat the process until the hair dye fades from the floor completely.