Kenyette Godhigh-Bell dismissed any thought of becoming a truck driver years ago when it appeared too daunting to break into a job where more than 90% of workers are men.

“You’ve got this cowboy-boot wearing, cigarette-smoking, tattooed or whatever white guy’s job,” she recalled. Now Ms. Godhigh-Bell, a 46-year-old black woman in sleek high-heeled boots, regularly pulls her 18-wheeler to Nebraska slaughterhouses so she can pick up beef and chicken for transport to grocery warehouses.

She...