I am not aware of any product that could provide bathymetry data for rivers, due several facts:
Deriving bathymetry from satellite data relies on optical data and is applied in coastal regions (see e.g. http://www.eomap.com/water-depth). These, in turn, strongly depend on or are influenced by qualtitative water aspects (e.g. turbidity) and dynamics (e.g. waves, currents etc.).
Rivers in paricular can have either a significant turbidity level or wave-dynamics and in most of the cases reflect both that hinders reflection from the river bed and hence the derivation of bathymetry.
Satellites are used to map global bathymetry from surface altimetry but at a very coarse resolution. GEBCO likely provides the best global free bathymetric data (http://www.gebco.net/) but is still only 30 seconds in resolution (so often around 800-800m resolution, which varies with latitude). Same for E-TOPO. While it works for some global or regional work, it is likely not good for what you need... the best option in your case could be to contact your national/local hydrographic services and see what they have for this region.
I'm not an expert on that but I have seen some approaches to derive river bathymetrie from remote sensing data. For sure you'll not find a ready product for rivers of India but if you are interested in the procedure check this:
Those large Indian rivers of Himalayan origin like the Brahmaputra which carry massive loads of sediments, go through rapidly changing bathymetry. Moreover, for braided rivers, channel patterns keep on changing very fast. If the objective is to study the thalweg variability, satellite imageries can definitely be used indirectly. For example, at a number of times, widest channels are also the deepest. Thus, studies in the plano-temporal variability can be related to changing definition of bathymetry. Direct measurement of depth variability may not give very good results as discussed by other contributors in this thread.