The couple was en route to the Country Music Awards in Dallas with the band's tour manager when a rear tyre blow-out sparked a fire.
The driver pulled over to the side of the I-30 freeway and the passengers all disembarked safely as firefighters raced to the scene to put out the flames.
It's still unclear why the tyre burst and how it set the bus alight.
Photos of the badly damaged vehicle and Scott sitting cross-legged on a grass verge, texting to let friends and family know she was OK, have been posted online.
Scott took to Twitter to report the scare, writing, "Our bus tire caught on fire and we had to evacuate very quickly. Everyone is safe and sound.
"It was me, my husband, our tour manager, and driver. Thanking God for our safety and the safety of all of those who helped put this fire out and keep us safe."
She also posted a photo of the badly-damaged tourbus.