There is an article in the new knitty on cochineal dyeing!
I didn't write it, but before you all hop to try it I want to add a couple things to it (and I want to point out that this is not a critique of the article at all, it had limited space in which to write):
-You can actually buy cochineal in multiple forms- bugs, ground, and extract. If you are working with ground or bugs you might want to strain the cochineal solution before adding it to the dyebath to prevent particles.
-The alum talked about is probably aluminum sulfate or potassium aluminum sulfate (which has fewer impurities due to being refined more). If possible, you should NOT let the mordant dry on the fiber after mordanting. I usually use about 10-20% WOG (weight of goods) for wools (less for finer wools, more for thicker wools).
-Cochineal is super super sensitive to pH. Acid and hard water will change the color as will cream of tartar.
-If you are absolutely sure your spin cycle on the washing machine will not tangle your yarn, use the spin cycle between rinses to get the dye out faster.