'Bung' has a few uses in English.
- It is a stopper of a bottle.
- It to throw.
But also it is a bribe or enticement.
The word bung seems to have become less popular over time (after a staggering peak in the 1820s) however the 'bribe' usage seems more modern. Where did the 'bribe' usage of the term come from?
A couple of examples
The BBC remained defiant in the face of Harry Redknapp's fierce denial of any wrongdoing last night and promised their investigation into bungs in football would deliver damning new revelations about some of the country's top clubs. source
and
The Labour first minister of Wales, Carwyn Jones, has described the agreement as a “straight bung to keep a weak prime minister and a faltering government in office” source
and even The Economist uses it here
Bribery offered an average return of 10-11 times the value of the bung paid out to win a contract