No one else in his family (father, mother, brother, sister, etc..) has a Texas accent. The little (maybe overplayed) accent he does have probably came from his wife, a real Texan.
from link below:
President Bush is known as a plainspoken man, a straight-talker. So how did a word like "kerfuffle" come out of his mouth? It's not an everyday word; it means a commotion or fuss. Bush casually used it during a question-and-answer session after a speech at the City Club here. ...
An aide said he has heard Bush use the word privately before, but not in public.
Listen to his father -- New England accent. But the Connecticut-born New England prep-school boy Bush somehow sounds like a West Texas farmhand? Uh, no.
My favorite evidence of Bush's accent being nothing more than a political device is his pronunciation of the word "rather." Most Texans -- hell, most Americans -- pronounce "rather" with the same A sound as "rabbit" or "bad." But not Bush. In his county club world, the A sound is more like an O, so it sounds like he's actually saying "rother." It's as funny to me as it is predictable. I've never heard him say it any other way.
http://www.mydd.com/story/2006/3/21/03436/7269
hmmm?