I couldn't seem to find this info anywhere, so I've decided to do some work to figure it out myself. So far I have the following data:
{bribe cost} = 2 * {EDR recruit cost} / {starting unit size} * {current unit size} * (1 + .2 * {unit experience}) * ({unit can join player's faction} ? 2 : 1) * ({unit can join slave faction} ? 1 : 2)
The presence of a fort, level of weapon and armor upgrades, and the Influence of the diplomat have no effect on the cost of bribery.
Going off of this, bribing becomes more powerful the more units are able to be in the Slave faction, and the closer Recruitment costs are relative to Upkeep costs in the mod being played