As women approach menopause, the patterns of their menstrual cycle lengths change. To study these changes, we need to jointly model both the mean and variability of cycle length. Our proposed model incorporates separate mean and variance change points for each woman and a hierarchical model to link them together, along with regression components to include predictors of menopausal onset such as age at menarche and parity. Additional complexity arises from the fact that the calendar data have substantial missingness due to hormone use, surgery, and failure to report. We integrate multiple imputation and time-to event modeling in a Bayesian estimation framework to deal with different forms of the missingness. Posterior predictive model checks are applied to evaluate the model fit. Our method successfully models patterns of women's menstrual cycle trajectories throughout their late reproductive life and identifies change points for mean and variability of segment length, providing insight into the menopausal process. More generally, our model points the way toward increasing use of joint mean-variance models to predict health outcomes and better understand disease processes.