Ensuring the safety of Vulnerable Road Users (VRUs) is a critical challenge in the development of advanced autonomous driving systems in smart cities. Among vulnerable road users, bicyclists present unique characteristics that make their safety both critical and also manageable. Vehicles often travel at significantly higher relative speeds when interacting with bicyclists as compared to their interactions with pedestrians which makes collision avoidance system design for bicyclist safety more challenging. Yet, bicyclist movements are generally more predictable and governed by clear traffic rules as compared to the sudden and sometimes erratic pedestrian motion, offering opportunities for model-based control strategies. To address bicyclist safety in complex traffic environments, this study proposes and develops a High Order Control Lyapunov Function High Order Control Barrier Function Quadratic Programming (HOCLF HOCBF QP) control framework. Through this framework, CLFs constraints guarantee system stability so that the vehicle can track its reference trajectory, whereas CBFs constraints ensure system safety by letting vehicle avoiding potential collisions region with surrounding obstacles. Then by solving a QP problem, an optimal control command that simultaneously satisfies stability and safety requirements can be calculated. Three key bicyclist crash scenarios recorded in the Fatality Analysis Reporting System (FARS) are recreated and used to comprehensively evaluate the proposed autonomous driving bicyclist safety control strategy in a simulation study. Simulation results demonstrate that the HOCLF HOCBF QP controller can help the vehicle perform robust, and collision-free maneuvers, highlighting its potential for improving bicyclist safety in complex traffic environments.