Sea level rise is perceived as a major threat to the densely populated coast of the Bay of Bengal. Addressing future rise requires understanding the present‐day sea level budget. Using a novel method and data from the Gravity Recovery and Climate Experiment (GRACE) satellite, we partition altimetric sea level rise (6.1 mm/a over 2002–2014) into mass and steric components. We find that current mass trends in the Bay of Bengal are slightly above global mean, while steric trends appear much larger: 2.2–3.1 mm/a if we disregard a residual required to close the budget, and 4.3–4.6 mm/a if, as an upper bound, we attribute this residual entirely to steric expansion. Our method differs from published approaches in that it explains altimetry and GRACE data in a least squares inversion, while mass anomalies are parameterized through gravitationally self‐consistent fingerprints, and steric expansion through EOFs. We validate our estimates by comparing to Argo and modeling for the Indian Ocean, and by comparing total water storage change (TWSC) for the Ganges and Brahmaputra basins to the conventional GRACE approach. We find good agreement for TWSC, and reasonable agreement for steric heights, depending on the ocean region and Argo product. We ascribe differences to weaknesses of the Argo data, but we also find the inversion to be to some extent sensitive with respect to the EOFs. Finally, combining our estimates with CMIP5‐simulations, we estimate that Bay of Bengal absolute sea level may rise for additional 37 cm under the RCP4.5 scenario and 40 cm under RCP8.5 until 2050, with respect to 2005.