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'.
As he scrambled to pick up the handgun, it fired, shooting Thomas Reddington in the leg.
Additional charges could be filed based on the results of toxicology tests, which have not yet been received.
Bishop was off-duty and was among revelers at the Mile High Spirits and Distillery nightclub in downtown Denver in the early morning hours of June 2, Denver police said in a statement. As he grabs the gun, it can be seen firing.
Booking documents do not indicate if Bishop has hired a lawyer.
Video from the June 3 incident shows Bishop landing a backflip at the Mile High Spirits bar, and reaching down to pick up the weapon that had fallen from his trousers. Even without that analysis, there was "sufficient evidence" to charge Bishop with assault, McCann said. One person was accidentally shot when he picked up the weapon and it discharged.
Reddington, who is now recovering at home from his gunshot wound, told Good Morning America that he had watched the footage a number of times and was still confused by how it managed to occur. After an arrest warrant was issued, Bishop turned himself in Tuesday, reported the Denver Post.
"It is shocking that the only shooting to ever occur at our establishment came about as a result of an Federal Bureau of Investigation agent entering our distillery tasting room carrying a loaded firearm without our knowledge, in violation of our rules", the statement read, in part.
'We sat down at one of those picnic tables, I heard a loud bang and I thought some idiot set off a firecracker, ' he said in his first interview.
It also said the wounded patron is welcome to complimentary drinks forever at the bar.