PARTIAL RETRACTION:
Having had an uneasy feeling that I was (partially) wrong on this, and risking and earful from PSB (take that light-heartedly, Peter), I just read this All Music Guide excerpt about Bob's contribution to Carolyn Hester's 1961 Columbia album:
In 1960 she made her second album, Carolyn Hester, for Tradition, the label run by the Clancy Brothers. This cast her very much in the thick of the folk revival, including such standards of the movement as "The House of the Rising Sun" and "She Moves Through the Fair, " sung in her high, almost shaky and girlish voice. In the early 1960s she was briefly married to author and folk singer-songwriter Richard Farina, who became friendly with Bob Dylan shortly after Dylan's arrival in New York.
While recording her third album (also, confusingly, titled Carolyn Hester) for Columbia and producer John Hammond in September 1961, she invited Dylan, then almost unknown, to play harmonica on a few cuts. His work on the album helped bring him to the attention of Hammond, who signed Dylan to Columbia as a solo artist shortly afterwards.
Now, I won't swear that these [three, according to Shelton] cuts were Bob's first studio work, only that they preceded Bob's first album and the subsequent Belafonte recording.
Surely, there's a site out there that spells this stuff out, no?
http://wm02.allmusic.com/cg/amg.dll?p=amg&sql=11:jifpxqq5ld6e~T1