Starting out with money would be unusual... it would be too obvious to the one being compromised.
Always better to start with something small - so small it doesn't seem possible that anyone could see it as a bribe. Incremental degradation of a person's soul takes time... start with a cup of coffee - a magazine clipping... I'm suspecting these top people they were also compromised with an ideology that flattered their sense of 'being special'... of having a 'mission'...
True, there are no doubt areas in the bureaucracy where the corruption is milder and participation is voluntary. But I suspect there are areas of the swamp where the pressure to go along with the corruption is formidable and direct.
If you refuse to go along on ethical grounds, you pose a serious threat to those who are already corrupted. They know you know, so your very presence puts them in jeopardy and they will have to deal with you one way or the other. Your career may reach a dead end and they can push you out that way. If not, they may turn up the pressure until you fear for your safety, and the safety of your family.
Or you can stay in and get rich.
I’m sure all the while, even the most corrupt ones have all kinds of stories they tell themselves about all the good they are doing for society, to justify their empire building.
I forget who said it, but someone said the ostensible reason for government is to provide public services, but the true reason for government is to gather all the people who need to be bribed into one place.
So DC is really just a one-stop-shop for graft.