Rewilding is an ambitious approach to conservation aiming at restoring and protecting natural processes. As the world is rapidly transitioning into conditions that have not been observed before, we need to be able to extrapolate and predict how natural processes would act under new conditions. Species distribution models have a good potential to inform rewilding decisions by the predictive modeling of potential species presence under various habitat conditions. A critical requirement when utilizing these models is to be able to express the uncertainty in the environment or its predictions. This study demonstrates the use of Bayesian statistical models to address this challenge. As a case study, we explore Bayesian logistic regression and Bayesian generalized additive models in order to predict suitable habitats for Asian elephants (Elephas maximus) until the year 2070 under the worst case working scenario of climate change. In this comparative study predictions of habitat suitability are solely based on climatic conditions. The results of the two Bayesian models are compared to two benchmark models, maximum-likelihood estimated logistic regression and random forest. We analyze and discuss trade-offs, relative advantages, and limitations of these modeling choices. The results of our analysis suggest that one configuration of Bayesian logistic regression gives the most robust predictions in this setting, which tend to correspond with the distribution of woodland biomes broadly similar to those in the species' historical range.