One of my companies competors get caught bribing. After investigation it was determined the company doesn't pay bribes and so this was a bad employee. The fines otherwise would have shut them down. This was used to justify sending me to anti bribery classes even though I don't do the type of work where I'm likely to have opportunities to bribe someone (or so I think?). I wasn't told who it was though.
When companies need to bribe, they bring consultants which get paid for a different service which is unrelated to what they are actually offering. The consultants charge a lot and bribe the agents on the government either through favours like enjoy our jet or penthouse in Italy or London and get this specific thing done or tell us where to send this cash to which country and which account #.
It's as simple as that. All that money is often written off in accounts as "promotional expense" or sometimes as a different line item under consultancy.
That's how it goes.