In reproductive epidemiology, there is a growing interest to examine associations between air pollution exposure during pregnancy and the risk of preterm birth (PTB). One important research objective is to identify critical periods of exposure and estimate the associated effects at different stages of pregnancy. However, population studies have reported inconsistent findings. This may be due to limitations from the standard analytic approach of treating PTB as a binary outcome without considering time-varying exposures together over the course of pregnancy. To address this research gap, we present a Bayesian hierarchical model for conducting a comprehensive examination of gestational air pollution exposure by estimating the joint effects of weekly exposures during different vulnerable periods. Our model also treats PTB as a time-to-event outcome to address the challenge of different exposure lengths among ongoing pregnancies. The proposed model is applied to a dataset of geocoded birth records in the Atlanta metropolitan area between 1999–2005 to examine the risk of PTB associated with gestational exposure to ambient fine particulate matter |$\lt 2.5\,{\rm \mu}$|m in aerodynamic diameter (PM|$_{2.5}$|⁠). We find positive associations between PM|$_{2.5}$| exposure during early and mid-pregnancy, and evidence that associations are stronger for PTBs occurring around week 30.