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.
Federal Bureau of Investigation officials have refused to release Bishop's name although he had been identified by other media outlets.
Denver District Attorney Beth McCann said further charges may be laid against the agent, depending on the outcome of a blood alcohol test. In a video, Bishop is seen dancing and then doing a backflip - during which his pistol dropped from his waistband and landed on the floor. He scrambles for the gun, which fires as he picks it up.
The FBI declined comment Tuesday "in order to preserve the integrity of the ongoing investigation", spokeswoman Amy Sanders said.
Bishop was showing off his moves in the center of a dance circle at Mile High Spirits bar on June 2 when he launched into a back handspring.
"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", she said.
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Authorities have not said what kind of gun the agent was carrying, or why it accidentally fired.
Bishop works out of the FBI's Washington, D.C., office, according to 9News.
"Then I looked at my leg and see some brown residue".
"I originally thought, like, when I found out I got shot it was an altercation I got hit in the crossfire of, because civilian casualties like that, those happen".
The bar also said the patron who was shot is welcome to complimentary drinks forever at the bar.
The firearm went off when the agent picked it up.