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Preclinical Alzheimer's disease (AD), the earliest stage in the AD continuum, can last fifteen to twenty years, with cognitive decline trajectories nonlinear and heterogeneous between subjects. Characterizing cognitive decline in the preclinical phase of AD is critical for the development of early intervention strategies when disease-modifying therapies may be most effective. In the last decade, there has been an increased interest in the application of change point (CP) models to longitudinal cognitive outcomes. Because patients' change points can vary greatly, it is essential to model this variation. In this paper, we introduce a BAyesian Bent-Line Regression model longitudinal data on cognitive function in middle-aged adults with a high risk of AD. We provide an approach for estimating the fixed (group-level) and random (person-level) CPs, slopes pre- and post-CP, and intercepts at CP for cognition. Our model not only estimates the individual cognitive trajectories but also the distributions of the cognitive bent line curves at each age, enabling researchers and clinicians to estimate subjects' quantiles. Simulation studies show that the estimation and inferential procedures perform reasonably well in finite samples. The practical use is illustrated by an application to a longitudinal cognitive composite in the Wisconsin Registry for Alzheimer's Prevention (WRAP).