OBJECTIVE: Suicide is a major cause of mortality in bipolar disorder (BD), yet its neural underpinnings remain insufficiently understood. Suicide risk is thought to involve impaired cognitive-emotional flexibility arising from fundamental disturbances in brain dynamics. This study aimed to test this hypothesis by characterizing the energetic and dynamical constraints underlying suicide vulnerability in BD. METHODS: We applied energy landscape modeling to resting-state fMRI data from 123 individuals with BD (61 suicide attempters, 62 non-attempters) and 68 healthy controls. Brain activity was modeled as transitions between functional states, enabling quantification of neural rigidity. Group-level comparisons and correlation analyses were conducted to identify attractor stability, transition patterns, and their associations with clinical and cognitive measures. RESULTS: Four dominant attractor basins were identified. Basins A and D showed progressively reduced appearance frequency and stability from healthy controls to non-attempters and suicide attempters. Increasing suicide risk was associated with greater neural rigidity, reflected in a more constrained transition architecture with shorter and more repetitive transition paths in suicide attempters. Lower stability of basin A was associated with higher suicide risk, with cognitive impairment statistically accounting for part of this association in mediation analyses. CONCLUSION: Suicide vulnerability in BD is associated with entrenched functional brain states, reduced transition diversity, and elevated energetic constraints that may limit adaptive brain-state reconfiguration. These findings provide a mechanistic account of neural rigidity and suggest that altered brain-state dynamics may serve as a potential biomarker of suicide risk in BD.