Inferring bargainers' private valuations on items from their decisions is crucial for analyzing their strategic behaviors in bilateral sequential bargaining. Most existing approaches that infer agents' private information from observable data either rely on strong equilibrium assumptions or require a careful design of agents' behavior models. To overcome these weaknesses, we propose a Bayesian Learning-based Valuation Inference (BLUE) framework. Our key idea is to derive feasible intervals of bargainers' private valuations from their behavior data, using the fact that most bargainers do not choose strictly dominated strategies. We leverage these feasible intervals to guide our inference. Specifically, we first model each bargainer's behavior function (which maps his valuation and bargaining history to decisions) via a recurrent neural network. Second, we learn these behavior functions by utilizing a novel loss function defined based on feasible intervals. Third, we derive the posterior distributions of bargainers' valuations according to their behavior data and learned behavior functions. Moreover, we account for the heterogeneity of bargainer behaviors, and propose a clustering algorithm (K-Loss) to improve the efficiency of learning these behaviors. Experiments on both synthetic and real bargaining data show that our inference approach outperforms baselines.