Sprinkle colors that bleed into icing
I see two factors involved in this process. The sprinkles' tendency to release their colors, and the icing's ability to absorb them.

Moisture is undoubtedly involved in the color transfer, so the drier the environment they're stored in, the less likely it will be to occur. Of course, this also means your cookies will become dried out sooner.

If you are able to acquire different brands of sprinkles, you may find that some are less likely to bleed than others.

You might also be able to control the color transfer by modifying your icing recipe to include less moisture, or allowing a period of time for the surface of the icing to dry before applying your sprinkles.

You could easily experiment with this the next time you make a batch of cookies. Apply the sprinkles to some of the cookies immediately, but wait a while before applying it to others.

If you wait too long to apply the sprinkles, they may not adhere as expected. Through trial and error, you might find the "sweet spot" of timing that minimizes color bleeding, while allowing for proper adhesion of the sprinkles.