Learning jazz bass requires a significant level of dedication. My approach was to abandon everything else in music except for my newly-acquired double bass, a couple of large books of standards and a bunch of CDs by Sinatra, Miles Davis, Bill Evans, Mingus, Monk, Coltrane, Duke, ad nauseum
The key is to learn to read changes and compose lines from them. Jazz has a great deal of b5ths, diminished chords, altered chord extensions and other sorts of chords you don't typically see in rock and roll or ordinary popular music.
I was lucky - I had 15 years of musical background when I dug into jazz. If you can afford it, get a teacher who knows the genre and buy some CDs that you like in the genre. Jazz is a big field, so post some thoughts about just what type of jazz you mean:
Be-bop (Charlie Parker; Dizzy Gillespie)
Big Band (Count Basie; Duke Ellington)
Hard Bop (Art Blakey and the Jazz Messengers; Mingus)
Cool Jazz (Miles Davis; west coast groups like Shelley Manne and his Men)
Fusion (Again, Miles Davis; Frank Zappa (!))
Modern Jazz (the Marsalis brothers; Christian McBride)
Dixieland (early Louis Armstrong; Preservation Hall Jazz Band)
Free Jazz (Ornette Coleman, Art Ensemble of Chicago)
Out there jazz (my term) (Sun Ra and his Arkestra)
Smooth Jazz (ask someone else)
Go to youtube and search on some of these names to get an idea of each genre.