Personally, I would bring it to a good guitar tech or a luthier and replace it with Tusq.
Not that costly, will be done properly and will probably last forever.
As a bonus, the Tusq material has a very low coefficient of friction and allows for a more accurate and easy tuning with your tuner pegs.
Oh, and Tusq is also very robust.
^THIS^ If the manufacturer/custom shop gives me a choice? I always go with a Tusq nut. And, with the exception of a brass nut on my '73 Rick 4001 ('cause, hey; it was the thing to do back then), every nut I've ever had to replace, was replaced with a Tusq.
For a Fender Jazz Bass? Tusq makes nuts expressly for a Jazz Bass. There will most likely be a minimal amount of fitting required (no two basses are identical, after all), but it should be as close to a drop-in fit as you can get...

