My regular shift ends at midnight; after giving report to the employee who relieves me and then changing I am typically on the road by 12:40ish. This is a college town with a 1am-ish last call, but I have yet to experience anything near a rush-hour.
Bicycling in the early am hours around here means that the roads are nearly empty, and I find that drivers treat me much, much better than when I pull the occasional day shift. They give me much more room on passing, oncoming turners tend to wait until I pass them, people almost never run reds/yellows/stop signs, and it seems like they all tend to stick closer to the posted speed limits. I find that when there is traffic drivers get aggressive while competing with each other, and it really pisses them off when you impede their path to getting a car length ahead or beating the next yellow.