Try white vinegar or lemon juice (directly from lemon, not the diluted stuff you drink). Peroxide also can work as a whitener.
Bleach can be dangerous, unless you have a bleach pen and are extremely careful about not getting it on the black portion (use tape around the edges to protect it a bit and clean it up)
If nothing else works, get a seam ripper and remove the bias tape, then replace it with new white bias tape (it comes in 3 yd packages).