It's not just less expensive fabric that will bleed. I had a Jinny Beyer pink fabric and have never seen anything bleed like that did. I have found that if I let fabrics dry then iron then put into very hot water most won't bleed any more. The Jinny Beyer fabric I had about 9 changes of water. It was still bright. My teacher said it's what they call overdye. I'm just glad that I persevered because I hate to think what it would have done to my quilt.
BTW I wash everything.