Let $X$ be bipartite mixed graph and for a unit complex number $α$, $H_α$ be its $α$-hermitian adjacency matrix. If $X$ has a unique perfect matching, then $H_α$ has a hermitian inverse $H_α^{-1}$. In this paper we give a full description of the entries of $H_α^{-1}$ in terms of the paths between the vertices. Furthermore, for $α$ equals the primitive third root of unity $γ$ and for a unicyclic bipartite graph $X$ with unique perfect matching, we characterize when $H_γ^{-1}$ is $\pm 1$ diagonally similar to $γ$-hermitian adjacency matrix of a mixed graph. Through our work, we have provided a new construction for the $\pm 1$ diagonal matrix.