I dyed three cotton T-shirts. Two of them were white with some dye stains from a previous dyeing project. One was pink and had some black ink stains on it. I used iDye for Natural Fabrics-True Red.
I agitated them in the washing machine on hot for 40 minutes (the package said to agitate for 30 minutes, the web site said more time would be better for bright colors and colorfastness).
The white shirts came out not quite red but richer than pink. The pink shirt came out bright red. The stains on all the shirts are still visible although not as obvious as they were before.
I washed and dried two more loads of laundry after the experiment and no dye got onto that laundry.
The big test still to come is whether the color will bleed when I wash these shirts with other items.