I did not experience the Dust Bowl of the 1930's, but I was a land surveyor in and about the Texas Panhandle during the drought of the mid-1950's. I spent a lot of time outside in whatever weather had come up.
Much of the time, the weather was as clear as a bell, as is characteristic of the dry conditions that give rise to dust bowls and the like. The dust storms in the Panhandle used to come in with the fast-moving cold fronts from the north that the folks down in Texas called "northers," or, when the bank of dust or clouds was high enough to refract light down its face, a "blue norther." The wind would pick up dust and appear to the north thick enough to be mistaken for a range of mountains if you didn't remember where you were. We could generally tell where the dust was coming from -- black meant Kansas; red, eastern Colorado; and yellow, New Mexico and south-central Colorado. The black always looked the more menacing, but the yellow was the more troublesome. It was extremely fine, almost like talc, and insinuated itself everywhere.
My parents lived in a relatively new house, and my mother was in despair because of the way the dust inside made the house seem gloomy. My father was infuriated because the stuff would settle thickly on the television screen because of the electric charge on the screen and on the dust particles. He could never remember and would try to clean the screen with a soft cloth. Often enough he would ground the charge on the screen, causing his teeth to hurt, and the dust to start clinging to him. We used to turn off the interior lights, and shine a flashlight parallel to the walls to find the little plumes where the dust was being blown through almost invisible pores in the plaster and paint.
It was a problem to drive if one were caught on the highway when one of these things came up since the air-filter would quickly clog and, when it was taken off, the carburetor would shut down quickly thereafter. Many people, particularly those who had lived through the 1930's, were quite adept at washing out automotive air filters, and stripping and cleaning their carburetors at the side of the road. This took a bit of courage, since the friction of the dust particles would sometimes create some strong electric currents that could suddenly erupt in storms of sheet lightning.
Of course, people can get use to about anything and end up complaining about the smallest things. A friend of mine picked up one day and drove all the way to Ciudad Chihuahua in Mexico because, so he said, he had grown sick and tired of grit in his chili. There were also an abundance of drought jokes, such as trees chasing dogs down the street. In 1951, when the force of the drought was first beginning to be felt, some Texas folk were in favor of solving the Kansas-Missouri flood problems with a couple of BIG pipelines to divert the excess water to Texas, where it was needed.
Curiously enough, the same northerly winds that had carried the dust into the Panhandle sometimes met high-level moisture that had come over the Rockies or the Mexican Cordillera, and the result was a rain that cleared the dust from the air. Of course, the way that it happened was that the raindrops would gather dust particles as they fell, and, but the time they reached the ground, the raindrops had become globules of mud.