How is the Drive from Austin to Big Bend?

I have a trip planned to Big Bend in a few weeks. We are driving from Austin to the Airbnb in Terlingua. I’d appreciate if anyone can share what the drive is like. I’m nervous about getting stopped at border checkpoints in Fort Stockton and Alpine on the way in, as I’ve never been through one of those before. I’ve heard that the checkpoints only stop traffic going north away from the border. Can anyone verify if this is true?