Especially as a Texas Governor (extremely weak when Bush took office - now a little stronger thanks to Bush and Perry), the experience thing would hamper him more than normal. Even IOTL, some of his presidential weaknesses are likely due to the somewhat truncated Executive experience the Texas Governor gets, especially because he didn't have authority over the other cabinet departments (plural executive).
If Bush was to be anywhere it'd be as a VP for a far stronger GOP candidate and a hungover Clinton ("Hillarycare" goes really bad, the Republicans take over as OTL or even more so), AND the economy still sucks).