Thin-layer covers easily crack under traffic load, shortening their service life. Incorporating fiber materials into the mix can enhance crack resistance thanks to their abundance, affordability, and flexibility. However, different types of fibers have different performances in bitumen and mixtures due to different material properties. To explore this problem, basalt fiber, polypropylene fiber, and glass fiber were selected in this paper. The surface characteristics, internal structure, and adsorption capacity of oily substances were observed via scanning electron microscopy and oil absorption rate testing. The effects of fibers on the high-temperature and low-temperature properties of styrene-butadiene-styrene block copolymer-modified bitumen were investigated using the dynamic shear rheometer and the force ductility method. Ultimately, through indirect tensile testing and semi-circular bending tests, and the introduction of the toughness index and fracture toughness, a comprehensive evaluation was conducted on how varying fiber types and content affect the crack resistance and toughness of bitumen mixtures. The results show that the density and dispersion of the bundle fibers are the key to the oil absorption capacity under similar internal and external structural conditions. The oil absorption rate of polypropylene fiber is the best, reaching 5.423. Fiber incorporation can significantly improve the high-temperature rheological properties of bitumen. At 4% dosage, G*/sinδ increased by about 107.04% on average at 76 °C. At low temperatures, the increase in fiber content leads to a decrease in bitumen elasticity, and the influence of glass fiber is more obvious. The area of toughness did not reach 2000 N·mm at 4% dosage. After adding fibers, the toughness index and fracture toughness of the mixture increased by more than 2% and 35%, respectively. The maximum increases in fracture energy and crack initiation energy of the mixture are 14.29% and 47.29%, respectively. It shows that the fiber enhances the toughness, crack resistance, and crack propagation resistance of the mixture. The research results can provide some reference for the application of fiber-reinforced bitumen mixtures.