I can answer that question for you. It is a 1959. The reason some believe it to be a 1960 is that some of the machines and the label were changed when the instrument underwent some refurbishment.
I cannot tell you exact details of the work but it was performed by the gent who used to maintain George Harrison's guitars. Herbie and Georgie were close and thus this is how the referral for the work to the 1959 Jazz Bass came about.
I know this because Herbie told me the story while sitting at his breakfast table years back when people first started questioning the lineage of Herbie's bass.