Fuel bias is as you described it. As the engine ages, it burns more fuel than a brand new one.
The fuel flow (and drag) corrections are entered into the FMS. This would allow the FMS calculated quantity not to disagree with the tanks totalizer. The figures are based off previous flights and engine tests.
Maintenance personnel can refine the database by entering correction factors for drag and fuel flow. (737 manual)
There are also "biases" to consider, depending on the make and model of aircraft. For example with Gulfstream aircraft, our flight planning experts typically add a 16% bias for flights of less than three hours. However, biases depend on the age of the aircraft, how the operator flies it, planned flight level, and speed.
So, it’s best practice for operators to compare actual fuel burns with flight plan burns to confirm accuracy. (Source)
Boeing does not call it bias when I checked the 787/737 manuals, but 'bias' is likely a flight planning software term.
(Source) From a flight planner for a flight sim.
(Source) Random real flight plan. Note: company software differs.
Boeing 787 FMS interface where the drag and fuel flow corrections are entered.