Large language models (LLMs) are increasingly deployed in global healthcare, yet their outputs often reflect Western-centric training data and omit indigenous medical systems and region-specific treatments. This study investigates cultural bias in instruction-tuned medical LLMs using a curated dataset of African traditional herbal medicine. We evaluate model behavior across two complementary tasks, namely, multiple-choice questions and fill-in-the-blank completions, designed to capture both treatment preferences and responsiveness to cultural context. To quantify outcome preferences and prompt influences, we apply two complementary metrics: Cultural Bias Score (CBS) and Cultural Bias Attribution (CBA). Our results show that while prompt adaptation can reduce inherent bias and enhance cultural alignment, models vary in how responsive they are to contextual guidance. Persistent default to allopathic (Western) treatments in zero-shot scenarios suggests that many biases remain embedded in model training. These findings underscore the need for culturally informed evaluation strategies to guide the development of AI systems that equitably serve diverse global health contexts. By releasing our dataset and providing a dual-metric evaluation approach, we offer practical tools for developing more culturally aware and clinically grounded AI systems for healthcare settings in the Global South.