I have had color bleeding in the past (years ago) and then I had to experiment with different glues and paint finishes to figure out which ones did not cause bleeding.
In most cases for me - most water based and acetone based glues or finishes would cause bleeding, oil based finishes did not. I did use thin CA to coat some woods and then use medium or thick to finish gluing up segments.
Which glue(s) are you using now that is causing the problem?
I have not had problems with Titebond type of white glue or epoxies. Spray adhesives (3M, Loctite etc) does well with laminates and parquet laminates without causing bleeding. But while spray glues work well, they take some getting used to in order to keep air pockets out - if doing numerous layers.