Stream‐subsurface exchange provides the opportunity for stream‐borne substances to interact with streambed sediments in the subsurface hyporheic mixing zone. The downstream transport of both solutes and colloids can be substantially affected by this exchange, with significant implications for contaminant transport and stream ecology. Several previous studies have demonstrated that bed form–induced advective flows (pumping) and scour/deposition of bed sediments (turnover) will often be the dominant processes controlling local exchange with the streambed. A new model is presented for combined turnover and pumping exchange due to relatively fast‐moving bed forms, i.e., when turnover dominates the exchange in the upper part of the bed where active bed sediment transport occurs. While turnover rapidly mixes the upper layer of the bed, advective pumping produces exchange with the deeper, unsecured region of the subsurface. The net exchange due to these processes was analyzed using fundamental hydraulic principles: the initial exchange was calculated using an existing geometric model for turnover, and then the later exchange was determined by analyzing the advective flow induced under the moving bed form field. The exchange of colloidal particles due to moving bed forms was also modeled by considering the further effects of particle settling and filtration in the subsurface. Experiments were conducted in a recirculating flume to evaluate solute (conservative Li+) and colloid (kaolinite) exchange with a sand bed. The solute and colloid exchange models performed well for fast‐moving bed forms, but underpredicted the colloid exchanges observed with lower rates of bed sediment transport. For very slowly moving bed forms it was found that turnover could be completely neglected, and observed colloid exchanges were represented well by a pure pumping model. In the intermediate case where turnover and pumping rates are similar, water carried into the bed by turnover is immediately released by pumping, and vice versa. Thus, while this work further elucidated the basic processes controlling solute and colloid exchange with a bed covered by bed forms and provided a fundamental model for exchange due to fast‐moving bed forms, exchange in the intermediate case where turnover and pumping tend to compete can only be bounded by current models.