My honest answer is this:
I don't believe it is something that will ever stop. This is an opinion that is based on the facts that we know regarding human nature.
First one must look at the core reason one may bribe another person. It boils down to selfishness. Someone committing an act of bribery is working towards something that will offer a means to their own end. This is simply part of the selfish side of human nature.
That's not to say that everyone is afflicted by the division between their morals, and their selfish needs. Plenty of people would never engage in a bribe, but it's I think it's pretty accurate to say, that there are an equal number of people who will just as quickly engage in bribes, without giving it a second though.
I hope this answer helps.