Bipedal robots have advantages in maneuvering human-centered environments, but face greater failure risk compared to other stable mobile plarforms such as wheeled or quadrupedal robots. While learning-based traversability has been widely studied for these platforms, bipedal traversability has instead relied on manually designed rules with limited consideration of locomotion stability on rough terrain. In this work, we present the first learning-based traversability estimation and risk-sensitive navigation framework for bipedal robots operating in diverse, uneven environments. TravFormer, a transformer-based neural network, is trained to predict bipedal instability with uncertainty, enabling risk-aware and adaptive planning. Based on the network, we define traversability as stability-aware command velocity-the fastest command velocity that keeps instability below a user-defined limit. This velocity-based traversability is integrated into a hierarchical planner that combines traversability-informed Rapid Random Tree Star (TravRRT*) for time-efficient planning and Model Predictive Control (MPC) for safe execution. We validate our method in MuJoCo simulation and the real world, demonstrating improved navigation performance, with enhanced robustness and time efficiency across varying terrains compared to existing methods.

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