I've heard of using Tide and bluing (washing liquid) on white dogs and white mane and tail hair. I think you should go for it.
You need to set the machine to delicate though, and definitely hang to dry
We don't have Tide :( i'm sure something similar would work and I definitely wouldn't want her shrinking in the tumbler!
Ooh! Cowboy magic, I didn't think of that, I have the spray for stable stains and it is awesome! I might have a look for the shampoo!