The problem of obtaining an approximating curve from a given set of data points appears recurrently in several applied and industrial domains, such as CAD/CAM, computer graphics and animation, medicine, and many others. Although polynomial blending functions are usually applied to tackle this issue, some shapes cannot yet be adequately approximated by using the polynomial scheme. In this paper we address this limitation by applying rational global-support blending functions, particularly rational Bézier curves. Our method is based on a nature-inspired meta-heuristic called bat algorithm, which has been recently introduced to solve difficult optimization problems. To check the performance of our approach, it has been applied to some illustrative examples of 2D and 3D curves. Our results show that the method performs very well, being able to yield a satisfactory approximating curve with a high degree of accuracy.