Freshwater from rivers influences Indian summer monsoon rainfall and tropical cyclones by stratifying the upper layer and warming the subsurface ocean in the Bay of Bengal. Here, we use {\it in situ} and satellite data with reanalysis to showcase how river water experiences a significant increase in salinity on sub-seasonal timescales. This involves the trapping and homogenization of freshwater by a cyclonic eddy in the Bay. Using a specific example from 2015, river water is shown to enter an eddy along its attracting manifolds within a period of two weeks. This leads to the formation of a highly stratified subsurface layer within the eddy. When freshest, the eddy has the largest sea-level anomaly, spins fastest, and supports strong lateral gradients in salinity. Subsequently, observations reveal a progressive increase in salinity inside the eddy within a month. In particular, salty water spirals in, and freshwater is pulled out across the eddy boundary. Lagrangian experiments elucidate this process, whereby horizontal chaotic mixing provides a mechanism for the rapid increase in surface salinity. A salinity budget also suggests that horizontal advection explains much of the change in mixed layer salinity. Further, the adjustment of this freshwater eddy triggers submesoscale dynamics which appear to be an integral part of the process of salinity homogenization. This pathway is distinct from vertical diffusive mixing and is likely to be important for the evolution of salinity in the Bay of Bengal.