Bribery is easier than blackmail..
Agreed, but the two often go hand-in-hand. The taint attaches even if literal "bribery" doesn't exist. None of them will admit to cronyism (which isn't literally bribery), but cronyism is rampant. None of them will admit that their function is to ponder legislation offered from outside of Congress, but that's common.
My point is that Congress wants "business as usual" to be hidden from the public. They aren't leaders, they are puppets. And the pecuniary reward for being a puppet is substantial. They crave the position for personal riches.
There is a form of bribery that is absolutely happening.
Rock the boat and the knives come out at election time. You get a heavily funded opponent with redistricting thrown in on top. The demo will do everything they can to defeat you. See Allen West for a recent example.
Play ball, and you run unopposed.
It is really quite simple.
Is this bribery? yes
Does it happen? yes
Is it illegal? Probably not.
Can we stop it? I seriously doubt it.