From Battlestar Wiki, the free, open content Battlestar Galactica encyclopedia and episode guide
"Bingo" (or "bingo fuel") is Viper pilot slang that indicates that their fighter's fuel reserves are too low to continue their mission and have the minimum amount of fuel necessary to return to their battlestar before running out.
A pilot usually makes the declaration to their wingman, CAG or battlestar by shouting "bingo fuel!".
A Viper that's out of fuel is virtually impossible to fly, yet Kara Thrace manages to do so after she is involved with an in-flight accident that severs her fuel line (TRS: "Torn").
The term can also be jokingly used to indicate that one is out of alcohol (TRS: "Unfinished Business").
- The usage of "bingo" in Battlestar Galactica is identically used in American military flight circles. In that context, the phrase "bingo ammo" means a ship's cannons have run out of shells.