So how did they know which car was going to be rented out? (spoilers)

That theory makes sense. While Michael (Jeff Bridges) and Oliver (Tim Robbins) were in the building fist-fighting, there was plenty of time for the conspirators in driving the van, or driving another car or truck containing the bomb, to drive up, plant the bomb in the truck of Michael's car (which explains why Oliver dragged Michael out of his car and away from it into the abandoned warehouse). Plus the voices on the walkie radio that Oliver has saying: "Liberty One, set" meaning from one of the conspirators (either the mailman or telephone repairman/bartender) that they finished transfering the bomb to the truck of Michael's car, and the voice of the female conspirator (probably the girl with the pony-tail hairstyle): "This is Shadow One, go" meaning that the path is all clear and the other van will be on it's way to the FBI building meaning that Micheal will follow it to their target. It is very possible that Oliver threw his fight and allowed himself to be overpowered my Michael and then revealed the location of their target so that Michael will drive right to it to follow the false van.

In the shot when Michael get back into his red car and pulls away after fighting with Oliver (it is easy to miss on the first viewing), but he backs up his car right into the camera where there is a close-up of the back of the car and that the rear of it looks a few inches lower then when it is last seen minutes earlier. Meaning, that something heavy (the bomb) is inside the trunk and Michael is too frantic to notice.