Accurate prediction of surgical duration is pivotal for hospital resource management. Although recent supervised learning approaches, from machine learning (ML) to fine-tuned large language models (LLMs), have shown strong performance, they remain constrained by the need for high-quality labeled data and computationally intensive training. In contrast, zero-shot LLM inference offers a promising training-free alternative, but it lacks grounding in institution-specific clinical evidence, making its predictions clinically misaligned and prone to instability. To address these limitations, we present PREBA, a retrieval-augmented framework that integrates PCA-weighted retrieval and Bayesian averaging to ground LLM reasoning in institution-specific evidence without requiring task-specific fine-tuning. Specifically, PREBA first encodes heterogeneous clinical features into a unified representation. It then performs PCA-weighted retrieval, weighting each dimension by its contribution to the variation across institutional cases, instead of treating them as equally informative, and conditions the LLM to generate multiple candidate predictions. Finally, Bayesian averaging consolidates these predictions with population-level statistical priors, yielding a calibrated estimate that remains stable and clinically plausible. We evaluate PREBA on four real-world datasets spanning different institutions and languages, using three state-of-the-art LLMs, including Qwen3, DeepSeek-R1, and HuatuoGPT-o1. PREBA consistently outperforms zero-shot inference, reducing MAE by up to 64.9% and raising R2 to as high as 0.63. It further attains accuracy competitive with, and on several datasets superior to, fully supervised ML methods, while offering greater interpretability through retrieved exemplars and explicit priors. The code is available at https://github.com/kanxueli/PREBA.

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