In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterising patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GP) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian Process Manifold Interpolation (GPMI) method accounts for the topology of the atria, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction, and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds.