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Many global climate models, including the Climate Forecast System version 2 (CFSv2), have a biased representation of subseasonal modes of variability of the Indian summer monsoon. For instance, they simulate a weaker summer mean monsoon low‐pressure systems (LPS) climatology, faster than observed northward propagation of monsoon intraseasonal oscillations (MISOs), and a systematic dry bias over Indian landmass. The Bay of Bengal (BoB), with its shallow mixed layers and unique thermal stratification, significantly modulates the convective activity in this region at subseasonal‐to‐seasonal timescales through modulation of sea surface temperature. The highly stratified upper ocean in the BoB is due to the enormous freshwater it receives from rains and rivers. A river routing model is coupled to the CFSv2 to account for the riverine freshwater and the improvements in modelling the upper‐ocean structure are analysed. Model simulations indicate that inclusion of temporally varying riverine freshwater improves the upper‐ocean state in the BoB and the observed mixed‐layer temperature gradients in the Bay are simulated reasonably after incorporating the time varying river runoff. This resulted in increased LPS lifetime and track density, and enhanced rainfall over central India. Better representation of the upper‐ocean stratification in the model leads to larger post‐convection shoaling of mixed layers at intraseasonal timescales, thereby forming thick barrier layers. Enhanced air–sea interactions restricted to the shallow mixed layer are associated with stronger vorticity, specific humidity and low‐level convergence to the north of the intraseasonal convection band. This enhanced low‐level moisture convergence north of the convection centre results in realistic northward propagation of MISO and aids LPS activity. It is demonstrated that better simulation of the upper‐ocean structure in coupled climate models can improve the representation of subseasonal modes of monsoon variability. These results bear important implications for operational forecasting. [ABSTRACT FROM AUTHOR]