In this article a new Bayesian regression model, called the Bayesian semi-parametric logistic regression model, is introduced. This model generalizes the semi-parametric logistic regression model (SLoRM) and improves its estimation process. The paper considers Bayesian and non-Bayesian estimation and inference for the parametric and semi-parametric logistic regression model with application to credit scoring data under the square error loss function. The paper introduces a new algorithm for estimating the SLoRM parameters using Bayesian theorem in more detail. Finally, the parametric logistic regression model (PLoRM), the SLoRM and the Bayesian SLoRM are used and compared using a real data set.