OMG he’s a Mainline Protestant! He worships at an Episcopal Church.
He is something of a universalist:

When asked if he thinks that he prays to the same God as those with different beliefs [specifically, “Allah”], Bush said, “I do.”
“I do believe there is an Almighty that is broad and big enough and loving enough that can encompass a lot of people,” Bush said, but he drew a distinction when it comes to those who perpetrate terror.

He eschews inerrancy:

When asked if he believes the Bible is literally true, the president said that he’s “not a literalist” when it comes to reading the Bible, but rather focuses on the important lessons he believes the Bible teaches.

He believes in evolution, in the normal mainline theistic way:

As for whether one can believe in the Bible and believe in evolution, Bush said he does, adding that “I happen to believe that evolution doesn’t fully explain the mystery of life.
“I think that God created the Earth, created the world,” he said. “I think the creation of the world is so mysterious it requires something as large as an almighty, and I don’t think it’s incompatible with the scientific proof that there is evolution.”

To my knowledge, this is the most forthcoming Bush has ever been about his faith. You wonder what his conservative evangelical supporters might have thought about him had he said as much six or eight years ago. You wonder what they may think now.