Document-level Relation Extraction (DocRE) aims to extract relations between entities across sentences, which requires more comprehensive reasoning abilities, such as commonsense reasoning and logical reasoning. While in-context prompting LLMs offers a zero-shot baseline, it often suffers from hallucinations and poor verifiability. We introduce a training-free framework that integrates a Bayesian-Adaptive Monte Carlo Tree Search (BA-MCTS) for iterative reasoning and refinement. A fast CoT prompt generates initial triples, which then undergo implicit reconstruction verification. If inconsistencies arise, a slow BA-MCTS process refines the results via Add, Delete, Modify, and Reason actions. The Bayesian-Adaptive mechanism dynamically adjusts exploration depth and breadth by evaluating semantic alignment and uncertainty, optimizing the search tree on the fly. Experiments on DocRED and Re-DocRED show strong gains in complex reasoning while reducing hallucinations, establishing a controllable and verifiable paradigm for DocRE without fine-tuning.