The New York senator is a front-runner among those seeking the Democratic presidential nomination. Bush is a Republican.
In an exclusive interview Tuesday, Bush told ABC's Charlie Gibson, "No question, there is no question that Senator Clinton understands pressure better than any of the candidates, you know, in the race."
Not that Bush is abandoning the GOP.
"I do believe our (Republican) candidate will beat her, if she happens to be the nominee," Bush said. He refused to give his opinion on which candidate would win the Republican nomination.
Hillary Clinton was first lady during the administration of her husband, President Bill Clinton, from 1993 to 2001. President Clinton defeated Bush's father as he tried for re-election as president in 1992.
Bush called the former first lady a "very formidable candidate," saying she and the former president "understand the klieg lights," ABC reported.
First lady Laura Bush said in the White House: "You know the pressure there is, you know the difficulties ... I think it was very helpful for us to have been ... around the White House as much as we were when (President George Bush's) parents served there."