You are asking a question about a supposed anarchist society, but the example you are giving is (I presume) not from such a society. Given that massive difference, my first inclination is to tell you that your bad time in traffic has nothing to do with anarchy. Given my particular desire to see civilization end, the car example falls particularly flat.
On second thought, as someone who has to drive pretty much daily for my job (frequently commutes of ~50 miles), and as a realist as opposed to a utopian, I both understand the frustration you experience and, even if cars (and my job) somehow were no more due to Collapse/Rupture/TheRevolution I don't think the behaviors that lead to people being shitty and entitled would somehow disappear. That is a different problem than one of mere traffic flow.
Shitty people are going to exist. I would posit that the sort of groups I would want to live in wouldn't allow as much space for big men to use their big-manness in such ways; they would be smaller scale, the social mores would be different, but that is largely intellectual masturbation. I also know that such things still happen sometimes, even in the anarchist scenes I inhabit. The best counters I have seen are people being willing to not be bullied or allowing this to happen to begin with. The danger here is that the line between not taking shit and the current call-out culture of identity politics is a thin one, so thin it is often impossible to discern when you are straddling it.
I would aim to create relationships where such roles are minimized, and, when interacting with the rest of the world, I would use a diversity of tactics depending on the situation.
