You have asked a very general question and I can only provide some general guidance. There is a Bayesian Inference Task View on CRAN that lists many options. I will also mention the rstanarm and brms packages which use the Stan software and allow defining models using syntax like the usual R formulas.
If you give more details about what you need to do, someone may be able to give more specific advice.
I am not sure what you mean by the null model for Bayesian regression. I am no expert on Bayesian regression but as far as I know the null model is a frequentist concept. Perhaps I am just showing my ignorance.