The stand-up bass on this track has always been credited by Sony to Russ Savakus - though on what evidence is not known; examining the studio records back in the 1990s, Michael Krogsgaard was unable to find any documentation of who played on this session. However, according to author Daryl Sanders, who has interviewed Charlie McCoy numerous times for his book That Thin, Wild Mercury Sound, McCoy remembers very clearly that the bass player was 'a black guy'.* That rules out Russ Savakus, and immediately suggests Bill Lee, who had backed Dylan on sessions for Freewheelin' and Bringing It All Back Home (and would indeed be in the studio again when Dylan came to record "One Of Us Must Know" the following January). Lee was actually a more likely choice for this "Desolation Row" session than Savakus, who had apparently not fitted in well with Dylan's unorthodox working methods in the studio;†; after the first day of the resumed Highway 61 Revisited sessions (July 29) he had been replaced by Harvey Brooks on bass guitar.
Perhaps just through oversight, Bill Lee was not among the personnel listed on the sleeve of the Highway 61 Revisited LP. Savakus was included in these credits, but this could have been on the strength of his involvement in the earlier session on 29 July. So when Sony compiled the track-by-track credits for The Cutting Edge, Savakus was perhaps assigned to the August 4th "Desolation Row" session purely because he was the only musician in the original personnel list who might have played the stand-up bass.
† See Bob Dylan: Highway 61 Revisited by Colin Irwin, Flame Tree Publishing, 2008, p.127