"It's problematic that a foreign nation is involved in our election system. Our democracy is only as good as people trust the results", he later added.
While not directly naming President Donald Trump, it appeared Bush was targeting him in his comments.
Trump has repeatedly denied collusion between his campaign and Russian Federation and dismissed the conclusions of USA intelligence officials that the Kremlin had interfered in the presidential election.
Multiple congressional committees are now investigating the intelligence community's assessment, as is the Department of Justice in a probe led by Special Counsel Robert Muller.
There are numerous investigations underway to determine whether the Trump campaign assisted the Kremlin in its efforts. After a conversation with Russian President Vladimir Putin in Hanoi, Vietnam, in November, Trump said Putin was "sincere" in his denials. That is why most of his actions aim at the return of Soviet hegemony. "That's why North Atlantic Treaty Organisation is very important". "He can't think, 'How can we both win?' He only thinks, 'How do I win, you lose?'" "Putin is a brilliant tactician who has the capacity to detect weakness and exploit it".
The White House did not immediately comment on Bush's remarks.
"The Russian government has made a project of turning Americans against each other", Bush said during a forum in NY in October.
Ingraham said Bush should understand - especially after the American people spoke in the 2016 election - there is no constituency for perpetual military intervention, open borders and unpoliced global trade deals.
"It is important for our economy and also important for our soul that the immigration system functions well".
Bush also stressed the need to back North Atlantic Treaty Organisation and other alliances the US has with the world.
Though Bush has avoided explicitly criticizing the Trump administration, he has voiced veiled opposition toward the president's "America First" platform.
"But they meddled and that is risky for democracy", he said, adding that Russian Federation had done the same thing during the Cold War and was adept at trying to manipulate opinion in the United States and Europe.