  This paper is a sequel to our studies \cite{ZZ} and \cite{YZZ} on Bismut
K\"ahler-like manifolds, or {\em BKL} manifolds for short. We will study the
structural theorems for {\em BKL} manifolds, prove a conjecture raised in
\cite{YZZ} which states that any {\em BKL} manifold that is Bismut Ricci flat
must be Bismut flat, and give complete classifications of {\em BKL} manifolds
in dimension $4$ and $5$.
