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Negotiation agents must infer what their counterpart values, update those beliefs over dialogue turns, and choose actions under uncertainty. End-to-end large language models (LLMs) can imitate negotiation dialogue, but their opponent beliefs are usually implicit and difficult to inspect. We propose BOND (Bayesian Opponent-belief Negotiation Distillation), a framework for auditable negotiation. BOND consists of an LLM-based Bayesian teacher that scores dialogue contexts against the six possible opponent priority orderings, updates a posterior over those orderings, and uses the posterior for menu-based decision making, as well as a smaller 8B student language model that emits both negotiation actions and normalized posterior beliefs as tagged text. In the CaSiNo negotiation dataset, BOND outperforms the state-of-the-art and achieves mean Brier score 0.085 over opponent-priority posteriors. The distilled student preserves much of this belief signal, achieving Brier 0.114, below the uniform six-ordering reference of 5/36, approximately 0.139. Compared with a 70B structured-CoT baseline, the significantly smaller 8B student model yields substantially better elicited posterior calibration. We further showcase auditability through posterior trajectories, belief-versus-policy error decomposition, and posterior-prefix interventions. These diagnostics reveal that distillation preserves a scoreable belief report more strongly than causal belief-conditioned control, making weak belief-action coupling visible, not hidden.