This work concerns the effective personalized prediction of longitudinal biomarker trajectory, motivated by a study of cancer targeted therapy for patients with chronic myeloid leukemia (CML). Continuous monitoring with a confirmed biomarker of residual disease is a key component of CML management for early prediction of disease relapse. However, the longitudinal biomarker measurements have highly heterogeneous trajectories between subjects (patients) with various shapes and patterns. It is believed that the trajectory is clinically related to the development of treatment resistance, but there was limited knowledge about the underlying mechanism. To address the challenge, we propose a novel Bayesian approach to modeling the distribution of subject-specific longitudinal trajectories. It exploits flexible Bayesian learning to accommodate complex changing patterns over time and non-linear covariate effects, and allows for real-time prediction of both in-sample and out-of-sample subjects. The generated information can help make clinical decisions, and consequently enhance the personalized treatment management of precision medicine.