Mechanistic models for sediment transport on hillslopes are needed for applications ranging from landscape evolution to debris-flow hazards. Progress has been made for soil-mantled landscapes; however, little is known about sediment production and transport in bedrock landscapes that often maintain a patchy soil mantle, even though slopes exceed the angle of repose. Herein we investigate the hypothesis that patchy soil cover is stable on steep slopes due to local roughness such as vegetation dams that trap sediment upslope. To quantify local sediment storage, we developed a new theory and tested it against tilt-table experiments. Results show that trapped sediment volume scales with the cube of dam width. Where the dam width is less than about fifty grain diameters, particle force chains appear to enhance stability, resulting in greater trapped volumes and sediment-pile slopes that exceed the angle of repose. Trapped volumes are greatest for hillslopes that just exceed the friction slope and are independent of hillslope gradient for gradients greater than about twice the friction slope. For neighboring dams spaced less than about five grain diameters apart, grain bridging results in a single sediment pile that is larger than the sum of individual piles. This work provides a mass-conserving framework for quantifying sediment storage and nonlocal transport in bedrock landscapes. Results may explain the rapid increase in sediment yield following wildfire in steep terrain in the absence of rainfall; as sediment dams are incinerated, particles become gravitationally unstable and move rapidly downslope as dry ravel.