It can be done, it's a little time consuming, but it can be done. Just follow these steps:
1: Find out what material the shirt is made out of. Buy white dye appropriate to the material.
2: Wash the shirt in hot water for the extra dirty cycle. Don't add anything but mild detergent, or half detergent you would normally use.
3: Re-wash shirt alone in hot-hot water, add in 1 cup of unscented bleach.
4: See the funky colors of the shirt as the bleach messes up everything and the base colors come out. Re-wash with 1 cup bleach.
5: Follow the directions on the dye and dye the shirt. Double the soaking time, or overnight, to let the dye set in completely.
6: Re-wash the shirt in hot water only. No detergent, no dye, nothing.
7: Look at how messed up the shirt is because the dye didn't take in some places. Get frustrated.
8: Cry yourself to sleep worried that you'll never get the costume done in time.
9: Re-dye the fabric one more time in the vain hopes that it'll work this time.
10: Break down in a fit of hystarics and drive to 17 different stores trying to find a white version of the shirt.
11: On the way home, come up with a REALLY AWESOME costume idea that would look great and all you'd need is a black shirt... like the one... aw krap!
12: Repeat step 8. Ben & Jerrys is your friend now.
Or, you could just get the white shirt to begin with, but where's the fun in that?