Estimates of fluvial sediment discharge from in situ instruments are an important component of large‐scale sediment budgets that track long‐term geomorphic change. Suspended sediment load can be reliably estimated using acoustic or physical sampling techniques; however, bedload is difficult to measure directly and can consequently be one of the largest sources of uncertainty in estimates of total load. We propose a physically informed predictive empirical model for bedload sand flux as a function of variables that are measured using existing acoustic or physical sampling techniques. This model depends on the assumption that concentration and grain size in suspension are in equilibrium with reach‐averaged boundary conditions. Bayesian inference is used to fit model parameters to data from eight sand‐bed rivers and to simulate bedload flux over the available gage record at one site on the Colorado River in Grand Canyon National Park. We find that the cumulative bedload flux during the 9 year period from 2008 to 2016 was 5% of the cumulative suspended sand load; however, instantaneous bedload flux ranged from as little as 1% of instantaneous suspended sand load to as much as 75% of instantaneous suspended sand load due to fluctuations in flow strength and sediment supply. Changes in bedload flux at a constant discharge are indicative of short‐term sediment supply enrichment and depletion. Long‐term average bedload flux cannot be expected to remain constant in the future as the river adjusts to changes in sediment runoff and the dam‐regulated discharge regime.