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".
Video taken of the incident shows Bishop's dancing as onlookers cheered him on.
The bullet Bishop fired ended up striking the leg of 24-year-old Tom Reddington, a fellow patron of Mile High Spirits who was seated at a picnic table nearby.
Denver's district attorney says he may face additional charges once the results of his blood alcohol test become available.
The FBI declined to comment Tuesday on the filing of the formal assault charge against Bishop.
Bishop, 29, turned himself in to the local sheriff's department and he was charged with the alleged assault on Tuesday.
Bishop is due in court for an advisement hearing on Wednesday.
He has not been formally charged by the Denver DA's Office.
Booking documents do not indicate if Bishop has hired an attorney. The agent was taken to police headquarters and later released to a supervisor with the Federal Bureau of Investigation.
According to Fox News, the suspect has since been identified as Chase Bishop.
The firearm went off when the agent picked it up.
"He's welcome at Mile High Spirits to enjoy complimentary drinks forever", they said in a statement published by KDVR.
Retired FBI supervisory special agent James A. Gagliano wrote for CNN that he understood the need for a young agent to blow off steam. Still, he said he was shocked at the agent's poor judgment. "Even before he lost control of it, you can clearly see the weapon's outline against his shirt in the video".
"And knowing he was armed, he may have elected to avoid the dance-off".