In the United States, 22 U.S. presidents were lawyers, including John Adams, James Monroe, John Quincy Adams, Andrew Jackson, James Polk, Abraham Lincoln, Rutherford B. Hayes, Benjamin Harrison, Richard Nixon and Bill Clinton, just to name a handful. The vast majority of U.S. Presidents had law degrees, although some did not end up practicing law.
Back before the concepts of wacky personal injury and tenuous libel suits, the practice of law was always considered to be a noble profession, if not the most noble. Law and politics went hand-in-hand and often lawyers were urged by their educated peers to seek political office.
Outside of the United States, many world leaders are/were practicing lawyers or law graduates prior to entering politics, including the British Prime Ministers Addington, Grenville, Percival, Canning, Disraeli, Asquith, Lloyd George, Atlee and Blair.
Historically, many of the worst leaders had no background in law but went headlong into politics with nothing more than inherited title or a business degree.
No comment on Bush, but he did actually hope to study law at UT and Harvard Law, but was not accepted into either school.