A bridge buddy was Starfleet slang for a friend who was a bridge officer on a starship. Such friendships were often regarded as valuable for one's prospects at promotion.
When the USS Cerritos crew were granted R&R time en route to the Kontaran system in 2381, Brad Boimler was dismayed to learn that Beckett Mariner, Sam Rutherford, and D'Vana Tendi had all already made plans with their respective bridge buddies. Boimler attempted to find his own bridge buddy by approaching Kayshon, then Shaxs, then T'Ana, then Carol Freeman, and finally Jack Ransom, only to fall short with all of them. (LD: "wej Duj")
Later that year, after Brad Boimler stood up to the Cerritos senior staff and demanded that they listen to Shaxs' suggestion for how to deal with rogue Texas-class automated starships, Shaxs assured Boimler that they were bridge buddies, to Boimler's delight. (LD: "The Stars At Night")