Timeline followback (TLFB) is often used in addiction research to monitor recent substance use, such as the number of abstinent days in the past week. TLFB data usually take the form of binomial counts that exhibit overdispersion and zero inflation. Motivated by a 12‐week randomized trial evaluating the efficacy of varenicline tartrate for smoking cessation among adolescents, we propose a Bayesian zero‐inflated beta‐binomial model for the analysis of longitudinal, bounded TLFB data. The model comprises a mixture of a point mass that accounts for zero inflation and a beta‐binomial distribution for the number of days abstinent in the past week. Because treatment effects appear to level off during the study, we introduce random changepoints for each study group to reflect group‐specific changes in treatment efficacy over time. The model also includes fixed and random effects that capture group‐ and subject‐level slopes before and after the changepoints. Using the model, we can accurately estimate the mean trend for each study group, test whether the groups experience changepoints simultaneously, and identify critical windows of treatment efficacy. For posterior computation, we propose an efficient Markov chain Monte Carlo algorithm that relies on easily sampled Gibbs and Metropolis–Hastings steps. Our application shows that the varenicline group has a short‐term positive effect on abstinence that tapers off after week 9.