Integrating fibers into asphalt mixtures improves their crack resistance and permanent deformation. Previous studies have found the effect of various fibers on asphalt mixtures, but bamboo fibers were not included. In addition to providing strength and toughness, bamboo fiber’s recycled nature saves resources and protects the environment. This study investigates the reinforcement effect by different particle sizes and contents of bamboo fiber on asphalt mastic. Three sizes (100 mesh, 200 mesh, and 400 mesh) and three contents (3%, 6%, and 9%) of bamboo fibers were selected to modify the asphalt mastic. The frequency sweep (FS), linear amplitude sweep (LAS), multiple stress creep recovery (MSCR), and bending beam rheometer (BBR) test were used to evaluate the linear viscoelastic properties, fatigue performance, rutting resistance, and cracking resistance of fiber-modified asphalt mastics, respectively. Results demonstrate that bamboo fibers have excellent stiffness-reinforced characteristics, increase the elasticity of the asphalt, and enhance the high-temperature stability and low-temperature crack resistance of the asphalt mastic but adversely affect the fatigue properties of the asphalt mastic. In addition, asphalt mastics exhibited the same crack initiation stage and different crack expansion behavior, and the fiber incorporation prevented further crack propagation. Burgers model was used to represent the rheological behaviors of the asphalt mastic with bamboo fiber, and the model parameters are estimated. Furthermore, the Burgers model results indicated that the fiber addition reduced the proportion of elastic compliance and viscous compliance but increased the proportion of delayed elastic compliance of the asphalt mastic. Finally, the statistical model obtained based on the statistical approach can appropriately fit the values of rheological parameters with different fiber contents and lengths. The optimal design solution is 200 mesh with 9% content.