Bruce covered the song only once:
1972-02-05 - THE BACK DOOR, RICHMOND
One show, with The Bruce Springsteen Band the sole act on the bill. The second of nine shows held at the club during February. The setlist is culled from a handwritten setlist that was auctioned on an online auction website in 2010. Although the document is undated, the songs listed indicate that it is most likely to derive from the late '71-early '72 period. Therefore, although Brucebase has placed the information here in reality it could actually be sourced from any time around October 1971-February 1972. The thirteen-song track list is a mixture of known originals, covers and several that remain unidentified. The Drifters' "Save The Last Dance For Me" is the first song listed, the earliest known performance. The Springsteen-penned "Southern Sun" was recorded during the Demo studio sessions in May-June 1972. Two potentially unknown Springsteen originals follow, before a song listed only as 'E - A (?)'. "Down To Mexico" (written as "Do Run Daddy") and "Magic Kind Of Loving" were both definitely performed during the Band's residency at The Back Door. "When You Walk With Me" could be another original. "She's A Woman" was played at Rutgers University in December 1971 and "She's Cool" is likely to be a cover of the 1966 song by Greek garage-rock band Loubogg. The last three songs listed could all be Springsteen originals, indeed "Down To The Riverside" is likely to be Springsteen's title for the song commonly known as "Grandpa's Gone Down", a moving acoustic track about his grandfather. The song features several occurrences of the phrase "down to the riverside".
SAVE THE LAST DANCE FOR ME / SOUTHERN SUN / MOON BEAMS / I'M THE ONE /
DOWN TO MEXICO / MAGIC KIND OF LOVING / WHEN YOU WALK WITH ME / SHE'S A
WOMAN / SHE'S COOL / WHEN SHE WALKS / DOWN TO THE RIVERSIDE / A STORY: Setlist may be incomplete or inaccurate.