Bridgers first debuted her cover of the late Prine's "Summer's End" during a livestream set for Pitchfork in April.
Last week, SiriusXM broadcast Bridgers' cover, and released the recording on YouTube.
"Summer's End" featured on Prine's final album, 2018's The Tree of Forgiveness. John Prine died aged 73 in April after contracting coronavirus.
As well as releasing her second album Punisher earlier this month, Bridgers also covered Bright Eyes' "First Day of My Life", and covered The 1975's "Girls" in May.
