The video shows Bishop's handgun falling to the floor mid-flip, then discharging into the surrounding crowd with a loud pop when he reaches to recover it.
Authorities did not initially identify the Federal Bureau of Investigation agent because he was not arrested at the time, Denver police community resource officer Marika Putnam said.
Bishop turned himself in to the Denver Sheriff Department on Tuesday morning after a warrant was issued for his arrest, according to Denver police.
Additional charges could be filed based on the results of a blood-alcohol content test, which has not yet been received, authorities said.
The agent, named by police as Chase Bishop, was performing a backflip in a nightclub when his gun fell out of his pocket and shot a bystander in the leg.
The FBI declined to comment on the case "in order to preserve the integrity of the ongoing investigation". Bishop then places the gun in his waistband and walks off the dance floor with his hands in the air.
Multiple sources told 9Wants to Know that Bishop is not assigned to the Denver office and works out of Washington D.C. "And that's when it clicked in my head, 'Oh, I've been shot'".
Spokeswoman Amy Sanders said: "The FBI will continue to fully cooperate with the Denver Police Department and the Denver District Attorney's Office as this matter proceeds through the judicial process".
"He's welcome at Mile High Spirits to enjoy complimentary drinks forever", they said in a statement published by KDVR.