Note that plea bargaining isn't even doable in many systems. Plea bargains are only really common in the US and a few other places. Many other locations require a full trial regardless. This is generally balanced with weaker rules of evidence and fewer restrictions on what prosecutors and police can get away with.

To try to answer the original question: I'm not sure plea bargaining ever makes sense in a purely Bayesian system because a plea bargain essentially shortcircuits an attempt to find out the truth.