Rotating superconducting bearings promise great potential in applications due to their frictionless operation. However, these bearings show a lower dynamic stiffness and damping coefficient compared to ball bearings. In this paper we studied a bearing consisting of a fixed YBCO ring and a rotating magnet above the superconductor. The influence of the magnet aspect ratio on the dynamic stiffness of the bearing was investigated in order to find an optimized size. To change the aspect ratio, we kept the inner diameter of the ring constant and reduced the outer diameter while increasing the ring height. In addition to these magnets, one magnet with a reduced cross-sectional area was studied. The aspect ratio selection was based on preliminary magnetic flux density simulations, which compared the magnetic flux density distribution and the potential radial force for different aspect ratios. To conduct the measurements, the field-cooled magnets were displaced in a lateral direction and then released, resulting in a damped oscillation. The dynamic stiffness constants were calculated for each bearing from the relation of three axis acceleration measurements for different field cooling heights. The comparison of the stiffness constants for the different bearings revealed an optimal aspect ratio for the given YBCO ring. This optimum is almost independent from the cooling height. The comparison between the two magnet rings with similar diameters and different heights was similar for the bearing characteristics at a low cooling height, whereas a significant reduction of stiffness was observed with a larger cooling distance. The difference is bigger for the magnet with a reduced height. The optimal aspect ratio as well as the stiffness dependence on the cross-sectional area was confirmed by simulations of the magnetic flux density distribution.