This is a given and is well known to Darksiders: a car tire will track imperfections in the road much more perceptibly than a motorcycle tire.

You've got to get used to that. And if you do.. you will develop the skills required for that while you are riding. If you can do this... you will be eligible for the cookie that the Darkside offers.

You will occasionally see uneven road in front of you... you should (and will) expect non-linear movement of the bike and you should (and will) adjust your counter steering accordingly to compensate. You will find that you'll develop enhanced counter steering reaction while running a car tire, and it eventually will become second nature; a non-event for you.

Been there (many of us) Done that (many of us).