Here we prove that every bipartite graph Gden">de"> which is not an odd length path satisfies den">de">. This is the first general constant upper bound on the irregular chromatic index of bipartite graphs. Combining this result with Przybyło’s result, we show that den">de"> for every graph Gden">de"> which admits a decomposition into locally irregular subgraphs. Finally, we show that den">de"> for every 16den">de">-edge-connected bipartite graph Gden">de">.