Can I assume you essentnially have a linear model of covariates (Bx) and a logistic transform?
If so, by using a relatively standard practice Normal prior on the Betas you get L2 regularization for free, or you can force L1 regularization by using a Laplace prior.
Some (quite old, possibly out of date) code dicussed here: How to add an L1 Regularization on the likelihood when use pymc3 to sample a MCMC although I expect you can probably find newer discussions / code approaches here too