Try buying some thin, stiff opaque plastic report covers, and inserting them in between as separators. The drug store usually has some of these. Or try wrapping each bulb in plastic wrap or a small plastic bag.
Yeah, I was kind of coming to the conclusion that I'd have to put in a barrier of some sort but hadn't thought about bagging the petals. Thanks.

FWIW, I'd actually have to do the plastic wrap or what have you during the dyeing (just uncovering the particular petal I'm working on) as the bleeding happened during the dyeing. I'd probably have to keep it bagged during the steaming. It actually didn't turn out too bad this time. If you look really, really closely, you can see where there's a bit of purple on the outside edge of the red center section where the dark blue came in contact with the red, but it kind of gets lost in the black outline.
Here's the latest (the one I showed tied). The definition between petals is definitely improving. Unfortunately, I managed to drop in in water before it was steamed, so the colors are kind of muddy looking. Long vinegar pre-soak (several hours), tightly tied (single wrap slip knot with extra knots to anchor it), thickened the black dye I use between the petals and for the mottling outside the mandala with Superclear. I also used a very fine brush to apply the black dye for the outlines with more control, instead of an eyedropper like I had been.
