I have use Cream of Tartar to remove rust stains, but not mixed with bleach. This is the formula I used and it worked very well.
Make a paste by mixing equal amounts of cream of tartar and salt with hot water. Rub the paste into the rust and let it set for 15 minutes. Wash with your regular laundry detergent.
I have not used this on colored fabrics only on whites so I don't know what effect it would have on the colors.