W. Bush's public sector experience was so token I'm not sure if it really counts. He would never have been Governor with having his father in the White House.
Had he still been the nominee, W Bush undoubtedly would have won the Texas gubernatorial elections of 1994 and 1998 even if Bush 41 had never been president, even if only considering
a) that Clinton was the incumbent president and the natural wave-election tendency of the American midterms,
b) the demographic changes and resultant political direction that Texas was undergoing at the time, and
c) the overall political mood of America in the 1990s. The real question is whether W would have won the Republican nomination for governor of Texas (or even ran for it at all) if his father had never been president.
Also, being twice elected and serving six years as the governor of the second-largest state in the country - with a population and gross domestic product larger than those of most fully independent sovereign states, and with the most crude oil production of all US states, and directly bordering the foreign country which provides the highest number of immigrants to the United States and the highest number of overall border crossings on a yearly basis - is hardly "token" when it comes to political experience.