Thouless charge pumping protocols provide a route for one-dimensional systems to realize topological transport. Here, using arrays of evanescently coupled optical waveguides, we experimentally demonstrate bulk Thouless pumping in the presence of disorder. The degree of pumping is quite tolerant to significant deviations from adiabaticity as well as the addition of system disorder until the disorder is sufficiently strong to reduce the bulk mobility gap of the system to be on the scale of the modulation frequency of the system. Moreover, we show that this approach realizes near-full-unit-cell transport per pump cycle for a physically relevant class of localized initial system excitations. Thus, temporally pumped systems can potentially be used as a design principle for a new class of modulated slow-light devices that are resistant to system disorder.