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 pounced on the weapon but accidentally squeezed off a single round. While backflipping, a gun fell from his waistband and, upon Bishop picking up the gun, it fired.
Prosecutors said that additional charges may be filed based on the results of a pending blood alcohol content analysis of Bishop.
In a bystander video obtained by KMGH, Bishop, who was off-duty at the time, can be seen dancing at 12:45 a.m. June 2 at Mile High Spirits Distillery and Tasting Bar as onlookers crowd around, smiling and laughing.
Special Agent Amy Sanders, a spokeswoman for the Federal Bureau of Investigation field office in Denver, declined to comment on Bishop's employment status with the agency.
"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", Sanders said.
Thomas Reddington, 24, who was hit by the bullet in the leg, told "Good Morning America" on Thursday that he was still confused by the incident. "And that's when it clicked in my head, 'Oh, I've been shot'".
"We sat down at one of those picnic tables - I heard a loud bang and I thought some idiot set off a firecracker", Reddington told ABC News later.
The firearm went off when the agent picked it up.
The bar also said the patron who was shot is welcome to complimentary drinks forever at the bar.