Giffords and her husband Mark Kelly had lunch Saturday with the former president and his wife Barbara, ABC News Radio reported.
Giffords and Kelly are on a seven-day, seven-state "Rights and Responsibilities Tour" to push for expanded background checks for firearm purchases.
The Bushes previously met the former Arizona congresswoman while she was recovering in a Houston hospital after Jared Lee Loughner shot her in the head and killed six others in Tucson in 2011.
Bush has his own history with gun control. In 1989, he issued an executive order halting the importation of some semi-automatic firearms after a massing shooting that killed five children in California.
He also resigned from the National Rifle Association after the organization compared agents of the Bureau of Alcohol, Tobacco, Firearms and Explosives to Nazis who harass gun owners.
Giffords and Kelly kicked off their tour Monday in Nevada, and have since met with legislators who, in April, voted against legislation that would impose tighter background checks, ABC News Radio said.