The airstrike on Sunday in Deh Bala district of Nangarhar province also wounded nine other civilians, said Burhanullah Shinwari, the deputy chairman of the Senate, who led the delegation.
The U.S. military on Sunday denied that any civilians were killed in the incident. .
On Friday, U.S. coalition spokesman 1st Lt. Nathan Perry said that "any loss of innocent life is tragic."
"I assure you that civilians are never targeted, and that our forces go to great lengths to avoid civilian casualties," he said. "This incident regarding the air strike on July 6th is still under investigation by coalition forces."
Shinwari said that 39 of those killed in the airstrike were women and children, including the bride.
The group was targeted twice on Sunday as they walked along with the bride from her village toward the groom's house in another village, Shinwari said.
The nine-man commission was dispatched by President Hamid Karzai to investigate the incident on Tuesday. They returned to Kabul on Thursday. The commission included officials from the Ministry of Defense, the country's intelligence agency and parliament.
Shinwari said the group gathered information from witnesses and victims' relatives.
All those killed in the incident were buried in one cemetery near the village where the attack happened, Shinwari said.
"They were all civilians, with no links to al Qaeda or the Taliban," he said.
The members of the commission gave relatives US$2,000 for every person killed and US$1,000 for those wounded, he said.
The issue of civilian casualties has caused friction between the Afghan government and U.S. and NATO troops, and has weakened the standing of the Western-backed Karzai in the eyes of the population.
More than 2,100 people - mostly militants - have been killed in insurgency-related violence in Afghanistan this year. More than 8,000 people died in attacks last year, according to the U.N., the most since the 2001 U.S.-led invasion.