The lengths of time between marriage and giving birth to the first child and the interval between births have a crucial role in women's reproductive health. The length of exposure time to conception is well recognized as a main determinant of fertility.This study is aimed to fit a Cox Proportional Hazard(Cox PH) model under a Bayesian framework. We use the Bangladesh Health and Demographic Survey (BDHS) data of 2004 and 2007 to analyze some key determinants of fertility of women in Bangladesh by fitting Cox Proportional Hazard (Cox PH) model for survival time data. The covariates are used in this study age of the respondent, education of the respondents, contraceptive use, media(listening radio, watching television, reading newspaper), currently working status of the respondents, religion, type of place of residence, division. Under the Bayesian network, the cumulative hazard function is modeled as a gamma process. The prior for the regression parameters for different covariates are considered normal distribution with mean and variance that are the estimates of regression parameters obtained from the 2004 data.We have that covariates have significant effect on waiting time to first birth of women after first marriage . We also obtain the frequentist (classical) confidence interval and the Bayesian credible intervals of the hazard ratios for different covariates group. The Bayesian credible intervals are found shorter than the frequentist confidence interval.