Concrete structures are constantly subjected to both static and dynamic loads. Hence, this study mainly focused on the strain rate effect on the bond behaviour between reinforced recycled aggregate concrete (RAC) and basalt fibre-reinforced polymer (BFRP) bars. Pull-out tests were conducted to investigate the bond performance between RAC and BFRP bars. The strain rates which indicate the static, earthquake, and impact loads were considered to investigate the strain rate effect on the bond behaviour. The bond mechanism was analysed according to the bond interface damage and bond stress–slip relationship. Furthermore, the bond stiffness, bond strength, and bond slip were examined. It is found that BFRP bars with different surface shapes induced different bond mechanisms. Although the high strain rate effect improved the bond behaviour, it changed the bond mechanism. Dynamic influence factors reflecting the strain rate effect were developed, and the corresponding formulae were proposed. It was confirmed that the proposed formulae can accurately predict the bond behaviour under different strain rates. Finally, a theoretical model that can simulate the dynamic bond behaviour between concrete and BFRP bars was proposed. The achievements of this study can provide reference for the dynamic bond design of BFRP bar-reinforced RAC structures.