I am so sorry this happened to you; that's a sinking feeling when you discover a bleed!!! A similar incident with hunter green/cream fabrics turned me into a rabid pre-washer. Others have mentioned using the best fabrics---here is a photo of a tub of water used to pre-soak black MODA fabric.

Good luck in your efforts to remove the bleed, and be sure to let us know the outcome!

Reading suggestions...and all good but did NOT work for me...I used blue chalk pounce and it did NOT come out. The company making the pounce/chalk suggested using vinegar which set the blue dye even more on my white quilt...ugh! She had me send the chalk and pounce back and never even replaced the $13 pounce. Tacky, at best.
I tried EVERYTHING...Synthropol, Retayne, Grandmas Stain remover, etc, etc.. Got a nod from a quilt restorer on what would work
WHAT WORKED: Washed in oxyiclean and did not rinse well, put some oxyiclean light paste that I made up over the worst of the areas, then put is out in the sun on thick grass...some air underneath... several hours....then washed again and did not machine dry. I did this a couple of times and it was almost completely out. Then I started using it (instead of a wall hanging) as a table cloth on my breakfast table and found that after several more washings (no heat dry), the blue chalk from the pounce was completely gone... I can now machine dry.

how about a color catcher?

If all else fails, rather than applique over it, what about taking fabric markers and turn the stained fabric into a print. Use a fabric marker of a similar color as the stain and make something simple like three dots in a triangle shape (one dot on each point of an imaginary triangle) scattered over the patch. The stain can then become part of the fabric. And it if washes out over time, the dots won't look like a mistake. I love fabric markers for covering up boo-boos! :-)

OMG...it keeps going from bad to worse! I turned the quilt over (the back is red/white/blue broad stripes with stars) and there are several areas (not just from the one bad block) where stuff bled through to the back! Will prob never do a block exchange again! I got some of the blue bleed out of the front with Oxi-Clean, and am going to try to wash again with a color catcher.

I think the ultimate solution is going to be....since I have 2 similar quilts, but the other didn't have the bleeding issues (50 states block exchange--25 blocks in each quilt) ...is to take the label off of the other non-bleeder, and donate that one. Then put the label on the bled quilt and give it to my friend, who hopefully will understand the imperfections. He isn't expecting a quilt gift anyway, and hopefully will appreciate the gesture, rather than my donating a damaged quilt.
:(

I, too, am a fan of Oxyclean.

Have you tried one of those stain/bleach pens? Try the pen on a similar fabric (scrap color and white) that has bled. Lay it on a small screen such as a sweater screen placed over a sink or bathtub. Take a little conditioner(yes hair) and apply to the color edge. Use the pen on the white or lighter color, let set(or it may start working immediately). Depending how it starts to work then rinse with warm water while it is laying flat on the screen. Yes I did say hair conditioner. I've also seen Dawn dish soap wash it right out. The reason for the screen is when you rinse with water, it goes down through the screen, if you try on a towel it can bleed again and there would be telltale color left. I wash everything I bring home. Goes straight into the washer on warm water and regular cycle. Prints with white get color catchers. I've seen colors bleed on prints with light to white in the same fabric. Would be one thing if the lighter would be totally but when it's haphazard and looks more like a stain, that bites.

This is the number one reason I'll never own a front loader washer. They simply do not use enough water in the wash to float away excess dyes.

I treated a few areas with a bleach pen, then am washing again with color catchers. Will report back. I also found a product called Carbona...supposed to remove color-run stains? Though I hate to go from worse to completely ruined!

I had red and white fabric that bled when I was prewashing a full load - it came out pink and red - used color catchers - be sure to follow the instructions - it all came out!