Well, I always wash my fabrics first, but I think you may have a salvageable piece here. First things first: when you get the binding completed, look it over really well and make sure to note all the spots you are seeing. I would recommend washing in a large bathtub if you can, as the less "scrunching" of the fabrics you can accomplish, the better luck you may have in avoiding any further dye transfer.
Use COLD WATER, it should help to set the color better.
By all means, toss a color catcher in with it; it may help.
Whenever I wash my fabrics, especially those with a very deep, intense or strong color, I throw in a couple handfuls of kosher salt and at least a cup or so of vinegar. This helps to "set" the dyes. You may be able to do that here, too.
Finally, once the piece is washed, go over it with a fine-tooth comb and see if there are any spots where the dye has bled and left it's mark. If that is the case, you may be able to get at it with some peroxide on a cotton swab with some success.
I hope this helps your situation. Please let us know what you tried and your ultimate success! Good Luck.