Officials say Silva -- who fought at Bellator 180 -- busted into a CitiBank in Queens on August 24 claiming to have a gun, and threatening to shoot whoever didn't cooperate.

Cops say Silva got away with around $50k in cash.

Silva was arrested, and charged with 2 felony robbery charges ... including 1st degree robbery while displaying a firearm.

SdS's attorney, David Fish, tells us, "We intend to show at trial that he’s not guilty of what he’s alleged to have committed. The allegations are very serious. I think Sergio has a lot of confidence in that the truth will come out at trial."

Silva, who was present in the NYC court, pled not guilty to both charges. He's due back in court in April.