Unstable cutting conditions limit the profitability in milling. While analytical and numerical approaches for estimating the limiting axial depth of cut as a function of spindle speed are available, they are generally deterministic in nature. Because uncertainty inherently exists, a Bayesian approach that uses a random walk strategy for establishing a stability model is implemented in this work. The stability boundary is modeled using random walks. The probability of the random walk being the true stability limit is then updated using experimental results. The stability test points are identified using a value of information method. Bayesian inference offers several advantages including the incorporation of uncertainty in the model using a probability distribution (rather than deterministic value), updating the probability distribution using new experimental results, and selecting the experiments such that the expected value added by performing the experiment is maximized. Validation of the Bayesian approach is presented. The experimental results show a convergence to the optimum machining parameters for milling a pocket without prior knowledge of the system dynamics.