Hi, Jo. Last year I dyed several red, white and blue shirts for my boss's family. As I recall, the best advice I have been given was to rinse in cold water with a few drops of synthrapol, followed by laundering in hot water and synthrapol. Prior to that, I think I did my pre-wash with just cold water. Somehow, adding synthrapol to the pre-rinse helped to prevent back bleeding onto the white. Here's one of the finished shirts:

Oh, yeah... I also remember that with these shirts, I was applying thickened dyes, and I think I let them dry completely before laundering. That might have contributed to the lack of bleeding as well.
Judy