AbstractSediment entrainment in bedrock rivers is a key process for river incision and landscape evolution. Bedrock riverbeds are typically comprised of both exposed bedrock and alluvial patches, meaning grains can be entrained from positions on both surfaces. The critical shear stress needed to entrain a grain will be affected by the topography that the grain is located on, as it determines grain pivot angle and exposure, and impacts the local flow profile. The aim of this pair of articles is to determine how the properties of bedrock surfaces with and without sediment cover affect the grain‐scale geometry of sediment grains, and consequently their critical shear stress. We report experiments using 3D‐printed scaled replicas of fluvial bedrock surfaces, with 0 to 100% additional sediment cover. For each surface, grain pivot angles were measured using a tilt table. In this first article, we report how surface roughness and grain pivot angle vary between surfaces and with different amounts of sediment cover, and we explore the relationship between pivot angles and different metrics for measuring surface roughness. We find that: (1) surface roughness is not necessarily a linear combination of the individual roughness of bedrock and alluvial areas, and the underlying bedrock topography can still influence surface roughness at 100% sediment cover; (2) pivot angles generally, but not always, decrease with increasing grain size relative to surface roughness; (3) changes in pivot angles with increasing sediment cover are best explained by changes in surface roughness at spatial scales comparable to the grain size; and (4) pivot angles are also best explained by roughness metrics that incorporate the direction of roughness with respect to the tilt direction, and the surface inclination. This work provides new insights into the processes behind grain entrainment in bedrock rivers that are critical for determining how landscapes may evolve.