Red Trim on Sweatshirt Bled Onto White Parts?

I have a moderately heavy zip-hoody sweatshirt (80% cotton, 20% polyester) with a white body and red sleeves, hood, and piping on the pockets. There are just a couple of spots and bleeding along the collar, as well as, severe bleeding along the pockets.

If I use RIT will it cause more red dye to be extracted and therefore further stain the white portions? Is the same true for the lemon method? I've only found tips for all-white garments needing dye removal.

My girlfriend washed it without me (I was going to wash cold delicate and hang to dry) on regular cycle with warm water and then normal heat in the dryer! But it has only been washed once. What can I do to fix the white portion? This is a NFL team sweatshirt that is no longer made! =[

Thanks in advance for you advice.

By Mady