Renewable power-to-ammonia (RePtA) has gained significant attention in recent years, as green ammonia is increasingly acknowledged as a sustainable, zero-carbon fuel. Meanwhile, distributionally robust optimization has become a popular method to address uncertainties in energy systems. However, the general reformulation approach for the distributionally robust model may lead to either a suboptimal solution or one that is excessively conservative. In this context, this paper presents a physically-bounded distributionally robust chance-constrained (DRCC) dispatch approach with the exact reformulation for power systems with RePtA. First, a comprehensive RePtA model incorporating the production, storage, and utilization of green hydrogen and green ammonia is embedded in the electro–hydrogen–ammonia coupled system. Then, an improved metric-based ambiguity set is introduced by enforcing physical bounds on the uncertainty of wind power while preserving the exactness, resulting in a bilinear optimization problem. Finally, an iterative alternating minimization algorithm is specifically designed to decrease solution conservatism by adjusting the resulting physically-bounded exact bilinear optimization model. Numerical results demonstrate the effectiveness of the proposed method.