Bridge operations was a general term describing the typical functions and procedures that took place on the bridge of a starship.
One of the sections of the bridge officer's test covered bridge operations. Deanna Troi passed this section in 2370. (TNG: "Thine Own Self")
In 2371, a crewmember of a Kazon-Nistrim raider claimed to have lost all bridge operations. (VOY: "State of Flux")
In 2372, to avoid talking with Kes after an awkward encounter, Tom Paris decided he and Harry Kim would pretend they had bridge operations to discuss. After Neelix offered them some Alfarian hair pasta, Paris used this excuse, but Kim was called to the bridge by Chakotay, leaving Paris open to confrontation from the Talaxian, who was in love with Kes at the time. (VOY: "Parturition")