Carrier phase observations can significantly reduce noise and address substantial clock bias noise that pseudo-range observations alone cannot resolve. However, carrier phase measurements face challenges with whole-cycle ambiguities and cycle slips. This paper explores the principles of bidirectional pseudo-range and carrier phase measurements and the methods for calculating clock bias. It proposes a new approach for sampling and extracting bidirectional carrier phase observations to mitigate the effects of link asymmetry due to inconsistent sampling times on clock bias measurement results. To address the technical challenges of whole-cycle ambiguity resolution and cycle slip detection and correction in bidirectional carrier phase time comparison, an improved pseudo-range method is used to enhance ambiguity estimation accuracy, while a Kalman filter is employed for real-time cycle slip detection. A vehicle-mounted test platform was developed to validate the dynamic time comparison performance. Compared to pseudo-range bidirectional time comparison, the carrier phase bidirectional time comparison improves accuracy by 71.3%, with the root-mean-square error of the measured clock bias reaching the order of hundreds of picoseconds.