I would use cold water with about a cup of salt....to set the dye if possible....and I would include one of those
dye catcher cloths. I forget what they are called but they grab ambient dye in the wash and rinse water/
And be sure to get it right out of the washer and into the dryer or on the line immediatly after the last spin.
It says washable....so I would wash it and scream to the store if it runs!
Linda C

Embroidery should be done with a polyester thread so it won't hold color if the shirt bleeds. I would do as the tag says.

Polyester...ie dacron, is the worst material for grabbing and holding coloir. It's one of the reasons why so many items that are "blends" get dingy looking.
Linda C

Thanks for all the responses. I tried the salt with the color catcher, and then right into the dryer and it came out beautifully! I've had the dye transfer happen to other garments and now I can prevent it. Thanks!!