Border detection of melanoma and other skin lesions from images is an important step in the medical image processing pipeline. Although this task is typically carried out manually by the dermatologists, some recent papers have applied evolutionary computation techniques to automate this process. However, these works are only focused on the polynomial case, ignoring the more powerful (but also more difficult) case of rational curves. In this paper, we address this problem with rational Bezier curves by applying the bat algorithm, a popular bio-inspired swarm intelligence technique for optimization. Experimental results on two examples of medical images of melanomas show that this method is promising, as it outperforms the polynomial approach and can be applied to medical images without further pre/post-processing.