Legal Question in Criminal Law in California

"Bar" isn't an acronym. In England long ago each courtroom had a physical bar in front of the audience which (with some exceptions) only attorneys were allowed in front of. Attorneys were called members of the bar, and the term is still used. Fwiw, most courtrooms still have physical bars, and non-lawyer spectators are still required to stay behind them.

The second half of your question doesn't make sense.

I wonder whether you have been listening to too much Coast to Coast AM.

The only acronym that I know of for BAR is Browning Automatic Rifle. The "bar" in bar exam is not an acronym, and has the meaning that Mr. Hoffman relates.