As robots become increasingly integrated into our daily lives, the interest in physical human-robot interaction (HRI) is rapidly growing. This interaction is no longer optional but a necessity, given the accessibility of robots. An electric bicycle (E-bike) is a prime example of HRI, demonstrating its relevance and practicality. The rider's active engagement, particularly in actuating the rear wheel, exemplifies the close physical interaction between humans and robotic systems. Our research focuses on developing a robotic bike designed to enhance both driving efficiency and steering stability by analyzing human dynamics. Our advanced algorithm has shown significant results, reducing human energy expenditure by 5.09% compared to conventional power-assist systems and by 11.01% compared to non-assisted bicycles. Additionally, the algorithm improves velocity and acceleration stability while reducing jerks, providing riders with an optimal user experience.