The field of behavioural biometrics stands as an appealing alternative to more traditional biometric systems due to the ease of use from a user perspective and potential robustness to presentation attacks. This paper focuses its attention to a specific type of behavioural biometric utilising swipe dynamics, also referred to as touch gestures. In touch gesture authentication, a user swipes across the touchscreen of a mobile device to perform an authentication attempt. A key characteristic of touch gesture authentication and new behavioural biometrics in general is the lack of available data to train and validate models. From a machine learning perspective, this presents the classic curse of dimensionality problem and the methodology presented here focuses on Bayesian unsupervised models as they are well suited to such conditions. This paper presents results from a set of experiments consisting of 38 sessions with labelled victim as well as blind and over-the-shoulder presentation attacks. Three models are compared using this dataset; two single-mode models: a shrunk covariance estimate and a Bayesian Gaussian distribution, as well as a Bayesian non-parametric infinite mixture of Gaussians, modelled as a Dirichlet Process. Equal error rates (EER) for the three models are compared and attention is paid to how these vary across the two single-mode models at differing numbers of enrolment samples.