Sunbrella is "solution dyed" which means the dye pigment is distributed thoughout the thickness of the fiber, not just on the surface. That is why Sunbrella holds its color so well. And it also means Sunbrella isn't as susceptable to fading as a result of bleach application. But by all means try a sample first.
I would follow the containers recommendation, which is to use about a cup per gallon of water and spray or better yet, take the bimini down and lay it on the ground upside down and fully saturate the fabric with the bleach solution. Leave it on for 10 minutes and then hose it off.
Bleach kills mildew quickly and just as importantly it bleaches out the dark stain as well, within minutes. So it is dead and invisible. Wash it off afterwards and it will be gone.
David