Corruption is a lot more complex than it appears. The tendency is to think that if you have moral upstanding officials that you can save the $86 billion, but corruption usually happens because someone is seriously underpaid. It isn’t even clear that corruption is even economically harmful in all cases. The classic example of “good corruption” is a black market in a centrally planned economy.
Focusing on the “money that you can save” by eliminating corruption is not a good idea, because you’ll usually find that fighting corruption will cost you more money (in the short term) than letting it stay. The negative aspects to corruption are less the direct costs, but rather the bad effect it has on institutions and public trust.
What does happen as an economy develops is things that used to take place under the table start taking place on the table. Instead of showing up with suitcases of cash, you hire lobbyists and make campaign contributions. It isn’t any cheaper, but it does allow one to keep track of which flows are socially productive and which one’s aren’t and to make sure things don’t get out of hand.
In the case of your ATM salesman, I doubt that ending the corruption would save anything in direct costs. For bribes to end, you’d have to have the bank dramatically increase the salary of the manager (and this is one reason Western banks pay a huge amount to managers), and you’d still have to spend a huge amount of time doing sales and marketing. The benefits wouldn’t be in the direct costs, but rather in the indirect costs. The manager is going to make decisions of which is the best ATM based on what is best for the bank rather than who gives him the most money. There is also the social benefit. If it is commonly believed that rich people got their money through honest means, it makes it less likely that people will wait to string them along the wall and shoot them.