The answer is really "As much as you can, it can never hurt."
I would start with the pentatonic scales, and the blues scale...These will prove really handy for funk (as well as a lot of other stuff).
Work on improvising with them, pentatonic minor is awesome for Funk, play lots of octaves and 5ths and 7ths
If you don't know what I mean by that then go here
http://studybass.com
and start reading.
You need to have a basic understanding of how bass works with chords...Study Bass will teach you that.
You should eventually know how to play a whole slew of arpeggios (broken apart chords) as well as The major and minor scales, modes, blues scale, pentatonic scales.......reading music.....
