We investigate the time-resolved photoelectric response of WSe2 crystals on glass and flexible polyimide substrates to determine the effect of a changed dielectric environment on the speed of the photodetectors. We show that varying the substrate material can alter the speed-limiting mechanism: while the detectors on polyimide are RC limited, those on glass are limited by slower excitonic diffusion processes. We attribute this to a shortening of the depletion layer at the metal electrode/WSe2 interface caused by the higher dielectric screening of glass compared to polyimide. The photodetectors on glass show a tunable bandwidth, which can be increased to 2.6 MHz with increasing the electric field.