We first study the suitability of behavioral biometrics to distinguish between computers and humans, commonly named as bot detection. We then present BeCAPTCHA-Mouse, a bot detector based on: i) a neuromotor model of mouse dynamics to obtain a novel feature set for the classification of human and bot samples; and ii) a learning framework involving real and synthetically generated mouse trajectories. We propose two new mouse trajectory synthesis methods for generating realistic data: a) a function-based method based on heuristic functions, and b) a data-driven method based on Generative Adversarial Networks (GANs) in which a Generator synthesizes human-like trajectories from a Gaussian noise input. Experiments are conducted on a new testbed also introduced here and available in GitHub: BeCAPTCHA-Mouse Benchmark; useful for research in bot detection and other mouse-based HCI applications. Our benchmark data consists of 15,000 mouse trajectories including real data from 58 users and bot data with various levels of realism. Our experiments show that BeCAPTCHA-Mouse is able to detect bot trajectories of high realism with 93% of accuracy in average using only one mouse trajectory. When our approach is fused with state-of-the-art mouse dynamic features, the bot detection accuracy increases relatively by more than 36%, proving that mouse-based bot detection is a fast, easy, and reliable tool to complement traditional CAPTCHA systems.