I have used DMC floss since I began embroidering almost (gulp!) 60 years ago and have never had a problem with it bleeding. Gosh! Can't believe I started so long ago!

Back 30-40 years ago embroidery threads tended to bleed, with all the improvements in processes and dyes that very seldom is an issue anymore. Unless you purchase some, cheap, off brand floss I doubt you will have any problems. DMC! VAldani, anchor, aurifil and sulky are ( some) of the good quality colorfast flosses. I'm sure there are others too

I only use DMC and have never had a problem with bleeding.