Mr. Bush, 57, says he urges them to act boldly, even if it causes them grief and costs them political capital.
"If they want to be elected and be popular, then they probably ought to go do something else," he said in an interview. "This takes a lot of hard work, and it's typically pretty controversial.
"What I try to tell people interested in starting down this path is [that] taking an idea, converting it into policy, turning that policy into law, and then executing that law is a process that's not dissimilar to a political campaign," he added. "You're going from start to finish. You have to be intensely focused on this."
Mr. Bush's work with state policymakers is hands-on.
Earlier this year, he phoned individual Oklahoma legislators to urge their adoption of a Florida-style program to provide vouchers to students with disabilities, according to his aides, a measure that eventually became law.