It depends what kinda paint you have on the wall. If you're wall is oil paint, it'll be a little easier. If it's latex, you may get the stain off along with some paint. A Mr. Clean Magic Eraser may work without taking off paint. You could also try rubbing alcohol or nail polish remover. Nail polish remover will probably take off a bit more paint. Don't use bleach. Hair dye is often made with ammonia, which when combined with bleach can create a toxic gas. It's always easier to remove dye from an unwanted surface when it's fresh.