Hello, emptyhead, and welcome back to Just Answer.
I have removed dark brown hair dye stains from clear plastic bottles by using a mixture of bleach and water. Fill the bottle 3/4 full with water and then add chlorine bleach (like Chlorox) to fill the bottle all the way. Then let the mixture sit in the bottle overnight or for at least several hours. The time it takes to remove the stains depends on the color of the dye.
Here is a great site, from the editors of Consumer Guide, with lots of tips for removing hair dye from all kinds of things:
I hope this answers your question. If you need more help with this, please let me know.
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