Bush was considered an underdog against Ann Richards. He wasn't "anointed" so much as Bud Selig was dragging his feet with regard to his plans, so Bush decided to run for Gov. Being a Governor is much, much more similar to the Presidency than being a legislator. Voters have strongly expressed that sentiment for decades.
The Bush family's plan was for Jeb to win in '94 and then run for President in 2000. His loss, and W's win, changed that formula. But it's factually wrong to claim W was the heir apparent all along.
That's true, for a long time it was actually Jeb who was seen as the heir apparent. Wasn't George W. more or less the dark sheep, vis-a-vis his drinking and partying, at least during the 80s?