Normal direction
One of the key lessons that using the Bridge command teaches is understanding the direction that surface normals face. Simply put, this is the way that the polygon is facing and getting it wrong can have big implications when using the Bridge tool. Some 3D software is more forgiving than others with normal direction, but if a bridge command is not connecting in the way that is expected, do not be surprised that normal direction is the culprit. Most 3D applications depict normal direction by not showing the back of a polygon, and many have the option to explicitly show the normal direction when a polygon is selected.