Bedrock river valleys are fundamental components of many landscapes, and their morphologies-from slot canyons with incised meanders to wide valleys with strath terraces-may record environmental history. Several formation mechanisms for particular valley types have been proposed that involve changes in climatic and tectonic forcing, but the uniqueness of valley evolution pathways and the long-term stability of valley morphology under constant forcing are unknown and are not predicted in existing numerical models for vertically incising rivers. Because rivers often migrate more rapidly through alluvium than through bedrock, we explore the hypothesis that the distribution of bank materials strongly influences river meandering kinematics and can explain the diversity of bedrock river valley morphology. Simulations using a numerical model of river meandering with vector-based bank-material tracking indicate that channel lateral erosion rate in sediment and bedrock, vertical erosion rate, and initial alluvial-belt width explain first-order differences in bedrock valley type; that bedrock-bound channels can evolve under steady forcing from alluvial states; and that weak bedrock and low vertical incision rates favor wide, shallow valleys, while resistant bedrock and high vertical incision rates favor narrow, deep valleys. During vertical incision, sustained planation of the valley floor is favored when bedrock boundaries restrict channel migration to a zone of thin sediment fill. The inherent unsteadiness of river meandering in space and time is enhanced by evolving spatial contrasts in bank strength between sediment and bedrock and can account for several valley features-including strath terraces and underfit valleys-commonly ascribed to external drivers.