Rivers commonly exhibit substantial variability in suspended‐sand concentration, even at constant water discharge. Here we derive an approach for evaluating how much of this variability arises from mean bed‐sand grain size. We apply this approach to the Colorado River in Grand Canyon, where discharge‐independent concentration of suspended sand varies by more than a factor of 23 (N = 1.4 × 10⁶). Theory predicts that where concentration is controlled by bed‐sand grain size, concentration and grain size in suspension will be inversely correlated (i.e., coarsening of the bed causes suspended sand to become coarser in grain size and lower in concentration). Although the observed correlation is negative, riverbed grain size accounts for only 40% of the variability in concentration. The residuals vary by an order of magnitude; they arise from other processes, such as changes in topography or distribution of sand that cause shear stress to change at constant discharge, changes in the fine tail of bed‐sand grain sizes or changing bedforms. Both bed sand and the other factors influence concentration for durations from less than 1 day to several years. Predictions of concentration based on bed‐sand grain size (N = 4 × 10⁴) are less accurate than predictions based on suspended‐sand grain size, probably because suspended sand is a natural integrator of sand‐transporting processes, giving more weight to those areas of the bed that exchange more sand with the flow. Although the causes of variability vary from one river to another, the approach illustrated here is applicable to any river in which concentration varies at constant water discharge.