If the dye is properly set the colors shouldn't run.
Some cautions about using dyes. When mixing powdered dyes, it is a good idea to work outside and/or wear a face mask. You do not want to inhale this powder. It is not good for your lungs. You don't want to work in an area that is not well ventilated. I also should wear surgical gloves just to keep the dye off my hands and out from underneath my fingernails, but I tend to forget them at some point. I don't have a good area to work with dye in my studio and it is usually too windy or too cold to work outside in Wyoming, so my silk dyeing experiments tend to come in great clumps. I have been asked to consign my veils to a local store, but I don't work in the quantities the seller needs. Most of what I paint I give to friends as gifts.
The silk paint I am currently using is a brand called Dekka Silk Paints. I've used paints I like as well or better, this just happens to be what I bought the last time. I am far from being an expert and am still experimenting with materials. I send my painted silks to a friend to be steamed. She does silk painting professionally so has the equipment and charges only a very small fee for doing the steaming for me. The steaming process is where you are most likely to have colors run- if the silk rolls are not properly wrapped when they go into the steamer, water creeps into the rolls and spoils the dye job. Silk painting is a crap shoot- sometimes the results are beautiful and sometimes they are better off being chopped up and used in fabric collages or the bottom of birdcages.
To put pictures of patterns on silk, I draw the design on paper, then transfer it to clear heavy plastic make a cartoon to place under the silk. I stretch the silk on a frame and trace the drawing with a dye resistant medium called gutta. I have also used templates made of this fabric- just trace the edges with the gutta. Once the gutta is dry, I mix my dyes (oh, how I love to mix dye and watch the colors bloom!) and use a variety of brushes to paint the silk. This involves touching the loaded brush lightly to the fabric and letting the dye flow onto the surface. If there is a gap in the gutta outline, the dye will flow right through it.
To get ombre or spectrum effects, I use a foam brush an inch or two wide. The silk is dampened with water to allow the dye to flow more quickly, then I just start painting color on color, letting one hue of dye flow into another to form secondary colors. Gotta be careful here and have some grasp of color theory or you might end up with a very muddy veil. Starting out with colors that are next to each other on the color wheel is generally a pretty safe way to go.
Salt dye is a matter of sprinkling salt on a piece of dyed silk while it is still wet. The salt crystals actually push away the dye, leaving patterns on the fabric. Table salt gives a much different effect than large salt like you spread on sidewalks in the winter.
The only problem I have found with silk painting is time and space! If I ever get around to retiring from my day job, it will take me two years to catch up on all the art projects I have planned. I took a silk painting class last year that also included painting dye onto velvet. If I had occasion to wear velvet clothing, every inch of it would be painted- the colors are beautifully saturated on velvet in a way that silk cannot come close to. I think I posted the picture I did of a boa constrictor but I don't recall what thread I did it on. The problem with painting on velvet, at least in the USA, is the connotation it carries of oil paintings of Elvis on black velvet.
Dye painting is nothing like Elvis oils, but...