Understanding the drivers of interannual streamflow variability in the Brahmaputra River Basin is essential for improved flood risk assessment and hydrological forecasting. In this study, we examine the influence of large-scale climate modes and atmospheric dynamics on the observed streamflow at the Bahadurabad gauge in Bangladesh over the period 1987-2021. Wet and dry years were identified using the 75th and 40th percentiles of annual streamflow, respectively, and seasonal mean streamflows were calculated for the monsoon (JJAS) and its sub-seasons: Early (May-June), Peak (July-August), and Late (September-October). A broad-scale circulation index representing Indian summer monsoon variability was developed and found to be strongly correlated with streamflow at Bahadurabad. ERA5 reanalysis data were used to examine integrated vapor transport (IVT), sea level pressure, and 850 hPa wind components to trace moisture pathways, while SST correlations were analyzed to explore ENSO-related signals. A Bayesian network framework was applied to evaluate the causal influence of key climate variables-precipitation, NINO1+2, NINO3, NINO4, Dipole Mode Index (DMI), West Pacific Index (WPI), and Madden-Julian Oscillation (MJO)-on streamflow. Bayes Factors were calculated for each covariate and interpreted using Jeffreys' scale at 95% confidence. Results show precipitation to be the most influential variable across all seasons, with NINO1+2 and NINO3 exhibiting substantial to strong influence, with negative associations in wet years and positive in dry years. These findings highlight the combined roles of regional precipitation and remote ocean-atmosphere interactions in shaping monsoonal streamflow variability in the Brahmaputra Basin.