Spatially resolved dust rings in protoplanetary disks are widely used to infer disk and dust physics from multi-wavelength continuum observations. Their interpretation, however, often neglects grain growth and the evolution of the size distribution, limiting the connection between observed ring profiles and dust-evolution parameters. Building on a physical dust-ring model that includes coagulation and fragmentation, we develop a Bayesian inference framework that jointly incorporates radiative transfer and finite angular resolution. When applied to two rings in HD 163296 and two in LkCa 15, our framework yields gas-dependent estimates of the key dust-evolution parameters such as turbulence strength α and the fragmentation velocity v_(rm frag) in a self-consistent way. Most rings admit both a low-α, low-v_(rm frag) branch with small grains, and a higher-α, higher-v_(rm frag) branch with larger grains. Typical low-α branches have α∼10⁻⁵--10⁻⁴ and fragmentation velocities of order cm s⁻¹ level, whereas the higher-α branches reach α∼10⁻³--10⁻² and fragmentation velocities of a few to 20 m s⁻¹. The observed broad and wavelength-dependent profiles near the ring peaks can be reproduced by intrinsically narrow dust rings. This new framework offers a more direct route from multi-wavelength continuum data to the microphysics of dust growth and trapping—a connection that can be robustly tested with future high-resolution observations at longer wavelengths.