Either a police car or a tank
The "no killing" rule leaves room for interpretation, which needs to be exploited for the best answer. Also the question only asks to get from A to B not what happens afterwards.
First let's look at the tank/bulldozer/anything armored option. Yes it kills people, but since there are no traffic rules, no sidewalk or park is safe for pedestrians and whether you are in a tank or a motorcycle or even horse, if you hit a pedestrian, good chance he will die (horses are dangerous, I have been riding). But in the tank at least you reach B. Who is gonna arrest you anyway? The police is stuck in traffic like the rest. Or are they?
Situation two, the police can move fast through the traffic to stop any offenders. Well in this case the police car is the best means of transportation for you to get from A to B.
Bear in mind the question is about a single person getting from A to B. Most of the other people are going nowhere.
And I agreed that the question is too broad. What means no killing, is it OK to be arrested afterwards, can the police catch you some other way?