There are some after-market colorants used to change grout colors, but the problem with many of them is stability. Granted, there isn't a whole lot of UV light that will reach the inner sanctum of your bath, but often times tile/grout/tub cleansers will cause these aftermarket grout colorants to fade.
Grout is derived from portland cement. Most tile guys I know of will use an acid stain to change the color of recently placed grout.
There are hazards with acids, both to your person and to your septic.
Sample to get the desired color. It's not easy. Just recognize that it's easier to reapply the stain to keep going darker, but more difficult to lighten the color...so don't overdo it on your first application.