That's the reason I use Isacord polyester thread for machine embroidery. Here's a link to learn about it:
http://www.amann.com/en/embroidery-threads/isacord.html
I never have to worry about colors bleeding and can wash items embroidered with it with clorox and have many times. The thread is comparable to high sheen nylon and that's absolutely all I use for embroidery. I did a lot of research before I decided on a brand to stock my new sewing room. My son purchased the entire color spectrum for me. I think you will be satisfied with it if you try it.