I'm on the same boat. I've begun playing jazz about 18 months now. I'm no expert but here are my sugestions so far:
There are many types of Jazz, Standard, bebop, Hard Bop, Acid, Fusion, you name it. Find the style you like. Check
this link for info on the many styles of jazz. I love Jazz Standards and do not like Fusion or later Miles Davis stuff.
Jazz Standards. Check this
Web Site. Very useful information about Jazz Standards.
The Jazz Fake Book. For almost every jazz gig or jam people take tunes from the Jazz fake book. They usually say "Let's play song XYZ on page 231" or something like that. It is a book with 400 pages full of jazz standards. It comes in many clefs and keys (remember some horns are tuned in Eb, Bb and so on). I have the bass clef one. Check
this link to see the book I'm talking about.
Listen to the best. For people that like Jazz standards, some of the best bass players are:
- Ray Brown
- Ron Carter
- Milt Hinton
- Niels-Henning Ørsted Pedersen
- Charlie Haden
Get their records and listen. Also, if there is a trumpet player you like, for example, check who is on the bass and get more from him/her.
Metronome and recorder. Get a metronome if you don't have one already. Get a recorder so you can record yourself and hear what you sound like. Jazz players tend to be more accurate than Rock and R&B, for example. One jazz guitar player complained that I was 'out of tempo' when counting the band in (1, 2, 3, 4...).
Jam with other people. Once you learn a few tunes get other people to jam with. Make sure to save yourself an embarrassment and ensure they are about the same level as you. Tell them up front what you can and cannot play. Jazz players can be very competent and might have little patience with rookies (Guess how I found that out...).
Be patient. Learning jazz is much like learning a foreign language.
Have fun!
FJ