Try using your washer on hot water mode. Worried about dye getting in your normal clothes? After you’re done with dyeing, wash the washer by throwing in a towel and some detergent. Just wash a towel like normal, and the should pick up all teh dye.
As usual, please be sure to read up on the dye process first to be educated before you dye-ve in! (get it? get it??)