For picking up roadkills, Conquest mode is probably the best. There tend to be more vehicles available than in other modes, and in more predictable locations.
You might also find that it's actually easier to pick up roadkills in armor than with a quad bike. Quads have a relatively low area to impact the target with, and you can get roadkills by trapping opponents against a wall or other obstacle with an armored vehicle.
That being said, the most important trick to getting roadkills is to drive a lot of vehicles. However, try not to make it too obvious that you're going for the roadkill. When you do that, you tend to move in a straight line towards opposing infantry, which makes you an excellent target, and it rarely works, since the guy on the ground can change direction a lot quicker than you can in the vehicle. You're better off just doing a lot of driving and picking up the kills in the course of the game.