In my own experience (which is not large with dying) I died some strips that didn't match the coloring of adjacent strips. And I did die a few accent strips. I found that the stain did not want to run across the water based glue line into the next strip. I used artist water color paint. There's a pre mixed brand (very strong) called Dr. Martins which you can get at larger art stores. Airbrush artist use it a lot.

http://www.dickblick.com/products/dr-ph-martins-radiant-concentrated-individual-watercolors/

Die vs. stain : http://www.finewoodworking.com/Materials/MaterialsAllAbout.aspx?id=2954

Dr. Martins does not use particle pigments but chemical stains to keep it very fluid.

Bottom line is I got no bleed when applying epoxy. Once trick you can use with plywood like okume is to pull a razor line along the art area so stain will not travel. I use an X-acto knife for that. You have to be cautious with the application. I use Q-tips. If you load up a brush and flood the area, you can cause a bleed. Forget masking tape. Dyes and stain will travel under it on bare wood. You can mask an area if you use and air brush and I have done that too with good results.

The reason some dye jobs will bleed with epoxy is that so much is applied that it is not fully absorbed into the wood and is floating on the surface. Most dyes are alcohol based and alcohol is a epoxy solvent.