  In this paper, metric reduction in generalized geometry is investigated. We
show how the Bismut connections on the quotient manifold are obtained from
those on the original manifold. The result facilitates the analysis of
generalized K$\ddot{a}$hler reduction, which motivates the concept of metric
generalized principal bundles and our approach to construct a family of
generalized holomorphic line bundles over $\mathbb{C}P^2$ equipped with some
non-trivial generalized K$\ddot{a}$hler structures.
