I wouldn't mess with the bump node settings.  Your brightness is coming from 2 places in the strands compound node, the Color mix node, and the AnisotropicBsdf node.  If those settings are not modified for lighter hair then the highlights will get blown depending on the lighting conditions.  I found that the first color chip on the Color Mix node should be changed to black from the default white.  That increases the contrast on GS's map.  On the AnisotropicBsdf, the Anisotropy channel value should also be toned down.  I won't address the TranslucentBsdf node but it should be connected to an AddClosure node, not a MixClosure node, according to posts in other web forums.