In order to map datasets measuring a diverse set of modalities to scRNA-seq reference datasets, we developed bridge integration, an approach for cross-modality alignment that leverages a multi-omic dataset as a bridge. We characterize specific compositional requirements for the bridge dataset, perform quantitative benchmarking analyses with ground-truth datasets, and demonstrate the broad applicability of our method to a wide variety of technologies and modalities. Finally, we demonstrate how to use atomic sketch integration to extend the scalability of our approach to harmonize dozens of datasets spanning millions of cells.