Allergan states on their webpage regarding Lumigan that "pigmentation change is due to increased melanin content in the melanocytes rather than to an increase in the number of melanocytes."
http://www.allergan.com/products/eye_care/lumigan.htm
Bimatoprost will darken your hair and skin a bit where you apply it, that's why putting it on the skin like for beard hairs won't be a good idea since the darkening of the skin could be irreversible. But on the scalp that shouldn't be a problem. I'd test it first in a small area and see if it helps at all.