Break open the bubbly and put on your favorite party dress because I believe that a celebration is in order...the red dye has come out of the dress!
Thank you all so much for your tips and tricks on getting dye out of fabric. I hope that none of you ever need them, but in the off chance that you do, check out the amazing comments on this post.
As for my little miracle workers, I ended up using a combination of synthrapol and color-catcher sheets. Synthrapol is a product that apparently is often used by dyers to get excess dye out of fabrics and it appears to have worked wonders in this case (and all with just two little cap fulls). And as for the color-catcher sheets? Well, there's no mystery there - they just soaked up whatever leftover dye came out of the dress. Oh, and I'm not sure if this made a difference or not, but I kept the dress wet until I was able to wash it with the synthrapol because I was afraid that the dye would set if I allowed it to dry.
Now excuse me while I go breathe a gigantic sigh of relief. Whew...