My bike corrects itself when I get hit with a gusty cross wind. I was really surprised at first that it was not a bigger deal, but cross winds do not really bother me as the bike just automatically leans into it and keeps going straight. The tires move left or right depending on the direction of the wind, but never more than 1/4 of a lane or so and my body barely moves at all, just leans into the wind a bit with the bike.
It sounds like not all bikes do that from the rest of these posts???