Yup, Fiebings Leather Dye. Black. Mask off your nut/binding, make sure the fingerboard is finish/varnish-free and clean (I'd already been using lemon oil, the board wasn't grimy). Oh, wear gloves.
Apply the dye with a Q-Tip, and do smallish areas, let the dye set up for about 30 seconds and wipe off any excess. I was a little concerned about the inlay dots on the neck as it's almost impossible to go round them...i was easily able to clean off the dye on top of the dots with a Q-Tip dipped in some methylated spirit.
Obviously I was concerned. Christ, it was a £4.5k bass. The results were very much what I wanted and there's been little dulling of the board since I did it.
Good luck!