Our location in the Milky Way provides an exceptional opportunity to gain insight on the galactic evolution processes, and complement the information inferred from observations of external galaxies. Since the Milky Way is a barred galaxy, the study of motions of individual stars in the bulge and disc is useful to understand the role of the bar. The Gaia mission enables such study by providing the most precise parallaxes and proper motions to date. In this theoretical work, we explore the effects of the bar on the distribution of higher-order moments - the skewness and kurtosis - of the proper motions by confronting two simulated galaxies, one with a bar and one nearly axisymmetric, with observations from the latest Gaia data release (Gaia DR2). We introduce the code ASGAIA to account for observational errors of Gaia in the kinematical structures predicted by the numerical models. As a result, we find clear imprints of the bar in the skewness distribution of the longitudinal proper motion μℓ in Gaia DR2, as well as other features predicted for the next Gaia data releases.