you have to remember that polygons are single-sided surfaces. 'normals' are the perpendiculars of this surface. Sometimes normals are flipped and so instead of facing outward they face inward. The problem you had was caused by some facing inward and the others facing outward. Maya was trying to account for this by twisting the bridge.
Anyway, the darker faces just need to be reversed. Select those faces, then go to normals->reverse 
go to the options and change it to selected faces instead of all. After that, all the normals will be facing the correct direction and a bridge tool will have proper results.