How can I make my bandanna less colorful?

Soak it in a light solution of bleach & water - I've faded some shirts this way (on purpose & by accident). You could just try a few drops of bleach in a sink of water and then leave your bandanna in the sink & keep checking on it every once in a while. If it doesn't fade or lighten in a few hours, take it out & add a bit more bleach & mix it well in the water and try again.