If you are from a small town, you may be familiar with friendly honks or waves people give from their cars. In Japan, it is the bow which is much more commonly seen, even with people you do not know. If you allow someone to enter into traffic ahead of you, expect a bow of thanks in return. You should respond in a similar fashion if someone shows you the same kindness.
Bowing comfortably will take some practice. You do not want to throw your neck out by dropping your head forward too quickly. Neither do you want to take your eyes off of the road for too long. The best bows are deliberate, not rushed, and sincere. It is best to practice when your car is in a stopped position.
As you go about your day, imagine times when common, humble Japanese phrases like
Being able to bow properly is not only physical. Bowing often involves releasing your ego in order to demonstrate respect or reverence for someone you barely know. Prepping yourself for the modesty required in daily life in Japan may take some time. Westerners, and Americans especially, have a tendency to think the world revolves around them and it may be difficult to break that way of thinking. Humility is often thought to be a sign of weakness in Western culture. Take stock of your own thoughts on these matters and be prepared to respond accordingly.