An alternate excuse could be that it’s not B.A.R., it’s just Bar.
In an old English court, there was a wooden fence – called the Bar – across the front of the court that separated the audience from the people actually involved in the trial. When a lawyer became qualified to argue a case in court he was “called to the Bar” and could go through the fence to be heard by the judge. Thus the “Bar Association” is the association of people allowed to plead at the Bar.
In England even today there are two types of lawyer – a “solicitor” who handles routine legal matters and prepares cases (and who are represented by the Law Society) and a “Barrister” who is a lawyer that specializes in actually arguing cases “at the Bar” (and is represented by the Bar Association).
In the early days of the American colonies there just weren’t enough lawyers for there to be Solicitors and Barristers, so the system never took hold over here, and all lawyers are permitted to do both types of law.
The word “Barrister” comes from his pleading ‘at the Bar’, not the other way round.