Bleaching will weaken the stitches and fabric, leading to premature wear. Dyeing the entire thing will be tricky -- the bleached spots will take the dye differently than the original surface -- but there are tactics for the best dye job, as I learned when I asked a similar question in this old thread.
I never did try dyeing that white Utilikilt. . . it's lurking at the very bottom of an ever-growing to-do list!
Proudly Duncan [maternal], MacDonald and MacDaniel [paternal].