Clarifying dynamic processes of materials is an important research topic in materials science. Time-resolved X-ray diffraction is a powerful technique for probing dynamic processes. To understand the dynamics, it is essential to analyze time-series data using appropriate time-evolution models and accurate start times of dynamic processes. However, conventional analyses based on non-linear least-squares fitting have difficulty both evaluating time-evolution models and estimating start times. Here, we establish a Bayesian framework including time-evolution models. We investigate an adsorption process, which is a representative dynamic process, and extract information about the time-evolution model and adsorption start time. The information enables us to estimate adsorption properties such as rate constants more accurately, thus achieving more precise understanding of dynamic adsorption processes. Our framework is highly versatile, can be applied to other dynamic processes such as chemical reactions, and is expected to be utilized in various areas of materials science.