Accurate real-time models of human motion are important for applications in areas such as cognitive science and robotics. Neural networks are often the favored choice, yet their generalization properties are limited, particularly on small data sets. This paper utilizes the Gaussian process dynamical model (GPDM) as an alternative. Despite their successes in various motion tasks, GPDMs face challenges like high computational complexity and the need for many hyperparameters. This work addresses these issues by integrating the information bottleneck (IB) framework with GPDMs. The IB approach aims to optimally balance data fit and generalization through measures of mutual information. Our technique uses IB variable selection as a component of GPLVM back-constraints to reduce parameter count and to select features for latent space optimization, resulting in improved model accuracy.