Ultrathin Bi₂Se₃-NbN bilayers comprise a simple proximity system of a topological insulator and an s-wave superconductor for studying gating effects on topological superconductors. Here we report on 3 nm thick NbN layers of weakly connected superconducting islands, overlayed with 10 nm thick Bi₂Se₃ film which facilitates enhanced proximity coupling between them. Resistance versus temperature of the most resistive bilayers shows insulating behavior but with signs of superconductivity. We measured the magnetoresistance (MR) of these bilayers versus temperature with and without a magnetic field H normal to the wafer (MR=[R(H)-R(0)]/\{[R(H)+R(0)]/2\}), and under three electric gate-fields of 0 and ±2 MV/cm. The MR results showed a complex set of gate sensitive peaks which extended up to about 30 K. The results are discussed in terms of vortex physics, and the origin of the different MR peaks is identified and attributed to flux-flow MR in the isolated NbN islands and the different proximity regions in the Bi₂Se₃ cap-layer. The dominant MR peak was found to be consistent with enhanced proximity induced superconductivity in the topological edge currents regions. The high temperature MR data suggest a possible pseudogap phase or a highly extended fluctuation regime.