The evolution of many mountain landscapes is controlled by the incision of bedrock river channels. While the rate of incision is set by channel shape through its mediation of flow, the channel shape is itself set by the history of bedrock erosion. This feedback between channel geometry and incision determines the speed of landscape response to tectonic or climatic forcing. Here, a model for the dynamics of bedrock channel shape is derived from geometric arguments, a normal flow approximation for channel flow, and a threshold bed shear stress assumption for bedrock abrasion. The model dynamics describe the competing effects of channel widening, tilting, bending, and variable flow depth. Transient solutions suggest that channels may take ~1--10 ky to adapt to changes in discharge, implying that channel disequilibrium is commonplace. If so, landscape evolution models will need to include bedrock channel dynamics if they are to probe the effects of climate change.