I am working on a red, white/cream, and blue quilt right now. I too was worried about bleeding. So for the first time in my life I washed fabric. These are the directions I used, Use a mild detergent such as Dreft, Woolite, or Orvus quilt soap. Use a short gentle cycle on warm wash, cool rinse setting. DO NOT USE FABRIC SOFTNER. You can either toss fabric in the dryer on perm. press until ALMOST DRY, or hang outside (I hung). Remove fabric from dryer or line and press.
I will make sure to add SEVERAL color catchers in the washer when I wash it JUST IN CASE!
Good luck!