Anderson originally planned to forgo electronics for the recording of Bright Red and instead focus on more organic instrumentation from bass guitars, accordions, violins, Brazilian percussion, and drums.

Anderson likened the final product to some of her music from the early 1980s and said that the songs on Bright Red were less structured compared to her more recent work.

The song "Beautiful Pea Green Boat" has additional lyrics from the poem "The Owl and the Pussycat" by Edward Lear (misspelled "Edwin" in the album's liner notes).

Lou Reed co-wrote "In Our Sleep" with Anderson and also contributed guitar and vocals to the song, which also featured drumming from Joey Baron, tambourine polyrhythms from Cyro Baptista, and synth textures from Eno.

Linda Goldstein, who served as Anderson's manager, expressed optimism that these formats, particularly album alternative, would lead to more commercial success.