Persuasion, a fundamental social capability for humans, remains a challenge for AI systems such as large language models (LLMs). Current studies often overlook the strategic use of information asymmetry in message design or rely on strong assumptions regarding pre-commitment. In this work, we explore the application of Bayesian Persuasion (BP) in natural language within single-turn dialogue settings, to enhance the strategic persuasion capabilities of LLMs. Our framework incorporates a commitment-communication mechanism, where the persuader explicitly outlines an information schema by narrating their potential types (e.g., honest or dishonest), thereby guiding the persuadee in performing the intended Bayesian belief update. We evaluate two variants of our approach: Semi-Formal-Natural-Language (SFNL) BP and Fully-Natural-Language (FNL) BP, benchmarking them against both naive and strong non-BP (NBP) baselines within a comprehensive evaluation framework. This framework covers a diverse set of persuadees -- including LLM instances with varying prompts and fine-tuning and human participants -- across tasks ranging from specially designed persuasion scenarios to general everyday situations. Experimental results on LLM-based agents reveal three main findings: (1) LLMs guided by BP strategies consistently achieve higher persuasion success rates than NBP baselines; (2) SFNL exhibits greater credibility and logical coherence, while FNL shows stronger emotional resonance and robustness in naturalistic conversations; (3) with supervised fine-tuning, smaller models can attain BP performance comparable to that of larger models.