The low temperature rheological performance of basalt fiber reinforced asphalts (FRAs) is studied using finite element (FE) simulations and experimentations. First, a bending beam rheological (BBR) test of the pure asphalt is simulated using Abaqus, to build a basic pure asphalt BBR model. The simulation results of the pure asphalt specimen, obtained using the viscoelastic parameters derived either from the Burgers transformation method (BTM) already available in the literature or from a novel mathematical iteration method (MIM), are compared with experimental data, to choose the most reliable approach. Second, a virtual 3D FRA model is generated using Matlab. Different simplification methods pertaining to fibers forming the bundles are considered to further compare the simulation results with the experimental ones. Some FRA models with different fiber orientations are simulated and compared. Finally, the pure asphalt and FRA samples are tested and simulated under short and long term aging processes. The results show that the BBR model of the pure asphalt with parameters obtained from the iteration method is closer to the original experiment. A larger creep stiffness and a lower m-value are observed when considering less fibers clustered in bundles. The results obtained in the BBR test are dependent on the effective contact area between fibers and asphalt. In agreement with intuition, the creep stiffness turns out to be higher when the fiber orientation is constrained to be horizontal, and it progressively reduces for models with randomly and vertically distributed fibers. The creep rate shows an opposite trend. Finally, aging can increase the creep stiffness and decrease the creep rate of pure asphalt and FRA, and it is suggested to consider less fibers to simulate the bundles in order to improve the accuracy of the FE models against experimental data.