I've often wished there is some way of knowing this before buying the fabric - especially when buying for Patchwork or Applique. I finally found the information. The process of checking if a fabric is colour - fast is called crocking.
Just take along a swatch of starch - free white cotton fabric with you when you go fabric shopping. You can test the material you want to buy by rubbing it on the white cotton fabric. Obviously, if it leaves a residue on the white fabric, the colour is going to bleed. Pure common sense!!!
Source of Information: Sewing and Textiles published in 1918, (The University of Wisconsin) Author, Annabell Turner ,B.S.