The superconducting properties of DC magnetron sputtered Nb, NbN, and MoN films deposited on Sb-doped bismuth selenide (BSS) topological insulator (TI) films have been studied. In this two-fold study, firstly, thick superconducting films of ~100 nm have been studied to find the modifications in the superconducting properties of the films caused by the surface morphology of PLD-grown BSS substrates. A drastic suppression in the critical current density has been observed in the bilayers, which has been ascribed to the strong influence of the substrate on the morphology of the superconducting film and the enhanced density of superconducting weak links. The temperature dependence of the critical magnetic field has been carefully analyzed within the purview of the Werthamer-Hohenberg-Helfand theory, taking into account the effects of spin paramagnetism and spin-orbit scattering. As the second part of the study, ultra-thin bilayers of NbN-BSS, with thickness of the order of the coherence length (~5 nm), have been grown to study the superconducting properties within the proximity regime. A ~3.5 K suppression in Tc has been seen in the NbN(5 nm)-BSS bilayer, due to a combination of interface roughness and superconducting proximity, while a suppression of 0.6 K has been observed in the BSS(6 nm)-NbN(5 nm) bilayer, which is surmised to be solely due to the superconducting proximity effect.