<p>Accurate opponent trajectory prediction remains a significant challenge in autonomous racing, where vehicles often execute aggressive maneuvers and sudden acceleration changes. Transformer-based architectures like Motion Transformer (MTR) have shown promise for vehicle trajectory prediction in structured environments such as highways and urban roads. However, they, along with LSTM-enhanced methods like MixNet, face limitations in predicting trajectories under the extreme dynamics of autonomous racing, often leading to increased errors and computational inefficiencies. To address these challenges, we propose two novel methods. First, BézierMixNet extends MixNet by utilizing Bézier curves to more accurately represent trajectories through a combination of reference paths. Second, we introduce BARTé, which employs Composite Bézier Curves to achieve both computational efficiency and high prediction accuracy in dynamic racing scenarios. Our methods are evaluated on extensive datasets from the DeepRacing Formula One simulation and real-world data from the Indy Autonomous Challenge. Compared to state-of-the-art models, BARTé reduces average displacement error by approximately 4%, longitudinal error by 48% while reducing computation time by 90%, demonstrating significant advantages for high-speed autonomous racing.</p>