This is an interesting thread for me. This is something I really want to do. I spent a long time yesterday afternoon talking with a lady who was selling hand dyed fabrics. She has a background as an artist and was very helpful and informative. She said she likes to use Dye-Na-Flow which is a textile paint that simulates a dye. She usually sprays the fabric with two or three colors and then squishes it up to create different designs. She said she then heat sets the color with an iron and then washes the fabric and has no bleeding or color loss.
I came home from talking with her and googled Dye-Na-Flow to see how expensive it is to get started. I found you can buy a starter kit at Amazon for around $10 with 9 colors in it (very small bottles, but enough to try it I think). My plan is to cut some fat quarters of white and try a few different colors to see how they turn out.
I'm attaching a picture of a piece I bought from her that I just love. I'm sorry it hasn't been ironed yet, but I still thought you might like to see it.