In this paper, we explore the hydrodynamic instability of free river bars driven by a weakly varying turbulent flow in a straight alluvial channel with erodible bed and non-erodible banks. We employ linear stability analysis in the framework of depth-averaged formulations for the hydrodynamics and the sediment transport. A significant fraction of the sediment flux is considered to be in suspension. The analysis is performed for the alternate pattern of river bars at the leading order followed by the next order, covering the effects of flow regime. We find that the unstable region bounded by a marginal stability curve depends significantly on the shear Reynolds number, which demarcates different flow regimes, and the Shields number and the relative roughness (particle size to flow depth ratio). The results at the next order stabilize the bars with longer wavenumbers. The variations of threshold aspect ratio with Shields number and relative roughness are studied for different flow regimes. In addition, for a given Shields number and relative roughness, the diagram of threshold aspect ratio vs shear Reynolds number is explained. Unlike the conventional theories of bar instability, the analysis reveals limiting values of Shields number and relative roughness beyond which the theoretical results at the next order produce infeasible regions of instability. The limiting values of Shields number and relative roughness appear to reduce, as the shear Reynolds number increases. © 2021 Author(s).