This research investigates the interannual variability of monsoon onset and withdrawal in Bangladesh, both of which are major climate features shaping multiple societal activities. There is considerable research on the monsoon timing in South Asia, but with much less focus on Bangladesh. We applied a local monsoon onset and withdrawal definition to observations and the latest-generation high-resolution gridded precipitation data from the Climate Hazards Center for the period 1981 through 2018. We analyzed the interannual variability in monsoon timing in Bangladesh and its teleconnection with the sea surface temperature anomalies (SSTA) over the Pacific Ocean (El Niño Southern Oscillation, ENSO) and the Indian Ocean (IO). The monsoon starts with early significant rains in northeast Bangladesh and propagates westward, and a similar pattern is observed for withdrawal, which tends to be more homogeneous in time and space. A high spatial and temporal variability in monsoon onset and withdrawal is observed in Bangladesh, with a within-country average range of around 1 month despite it being a country of relatively small size. The association between monsoon onset and withdrawal and ENSO and IO is addressed at the country and regional level by analyzing composites for different ENSO and IO phases and associated atmospheric circulation and moisture transport. A similar association between monsoon onset and ENSO and IO phases was found, with generally earlier (later) onset dates during the negative (positive) phase of ENSO and IO. Monsoon withdrawal shows a clearer association with ENSO, with earlier (later) dates during the positive (negative) phase. Monsoon withdrawal is earlier during the negative IO phase. SSTA-induced anomalies in circulation and moisture transport contribute to anomalies in monsoon timing. Results suggest both ENSO and IOD can be potentially used as sources of predictability of monsoon onset and withdrawal over specific regions of Bangladesh.