What should/can we as US citizens do to stop lobbying which is basically legalized bribery?

Term limits! Career politicians have been there too long while passing laws that give them special privileges and immunites. They've been there long enough to develop too many closed-door, interpersonal relationships with the lobbyists/special interest groups.

Lobbying to advocate for this issue or that policy is as American as apple pie, and indeed is what our Representatives should do, meeting with constituents.
The problem lies in the money, especially in self-licking ice cream cones like Civil Servant unions and defense contractors.
The problem you have is a Supreme Court decision that says that corporate and individual campaign contributions are 1st Amendment protected speech. Direct bribery is a crime. Indirect bribery however... not so much.
While we are at it, we need to look at Congressional Insider Trading as a crime, which they have a specific statutory exemption for. It is not a coincidence that getting elected to Congress means becoming wealthy, even though the pay itself won't get you there. These two items are largely the reason why.

The fact that neither party really is pushing hard for lobbying reform tells you most of what you need to know. They like being winded and dined and are not motivated to stop it. They also line up nice careers once they leave congress. It will take a major change in Congress (like term limits) before it gets addressed.