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It is known that an ordered \(\rho\)-labeling of a bipartite graph \( G \) with \( n \) edges yields a cyclic \( G \)-decomposition of \( K_{2nx+1} \) for every positive integer \( x \). We extend the concept of an ordered \(\rho\)-labeling to bipartite digraphs and show that an ordered directed \(\rho\)-labeling of a bipartite digraph \( D \) with \( n \) arcs yields a cyclic \( D \)-decomposition of \( K_{nx+1}^* \) for every positive integer \( x \). We also find several classes of bipartite digraphs that admit an ordered directed \(\rho\)-labeling.