Songwriters Annie and Sam Tate, who are husband and wife, co-wrote the song with Rivers Rutherford.

"Shut Up and Drive" is composed in the key of A-flat major with a main chord pattern of A♭-D♭-A♭-E♭-A♭.

[2] Brian Wahlert of Country Standard Time described the song favorably in his review of the album, saying that it "simmers with a combination of sympathy and quiet urgency until Wright wails demandingly on the chorus, 'I'm the voice you never listen to/And I had to break your heart to make you see.

It shows Wright performing the song in a loft, as well as her driving a VW Beetle Convertible through many sceneries.

A traffic jam scene is then shown, and as she patiently waits for it to clear, her boyfriend runs up to her car, but she finds an open lane and drives away, leaving him in the dust.