Fleeing bank robbers attempt to deliver stolen loot to a corrupt politician on the GW bridge, but when things go wrong…they take hostages.

Action/political satire. You have great ideas, and it's well said. I'm better at writing it, than explaining, and that's not good.

Christopher, I understand that you want to use the bridge gate as a backdrop to your script. But from you latest point, the movie is not anymore about the bank robbery. It is more about corruption and collusion. It is about the investigation into the bank robbery revealing that corruption and collusion. So the logline should reflect that change in emphasis. For example the main character should be an observer or the investigator.
When investigating a bloody bank robbery shoot out on packed high way, an idealist journalist discovers that political corruption and collusion have played a major role in the incident. She must recover the evidences and convince her sceptic editor before dark forces shut her forever.
That script could use the fact the bank robber were foiled in their attempt to escape by the bridge gate. During the ensuing shoot out, numerous people are killed. Now everybody is trying to cover up the fact that the traffic was manipulated to create a traffic jam. The politician who is responsible for the manipulation plays the media. He offers his help to the police in resolving the hostage situation. In the mean time, his fixer is cleaning up the problem.
Is it what you had in mind, because that it did not translate in your logline?
Natural Born Killer is a very good satire of the cult of the media.
What genre is your movie: action, satire, drama, comedy?

It's true that fans outside the US wouldn't know, until he runs for president. The scandal will emphasis the theme of the story, by using the media's obsession with corruption to either aid/prohibit the characters.