Jazz can be daunting when ya don't know what's going on. I have played jazz guitar since the early 60s, 6-nights-a-week in the 70s and jazz bass since 1988. At least by the time I was mainly a bass player I had a background. Mostly standards and some jazzy blues. But, what to do for bass lines? Well, I just used my noggin and theory degree to do the very things outlined above in Ed's post. It was just intuitive to proceed with ideas like that. I listened some, but really never dug too deep into anyone in particular as far as style goes. I figured I could figure it out, and I did.
It helps to know theory. Or, maybe I should say it is essential. I couldn't get by without it, myself. I have sat many an hour with the Real Book playing through the changes and doing one thing more that hasn't been listed---singing the melody along with the bass line. Eh, humming, that is. Sometimes the bass line on its own needs to hear the melody as well, especially when the melody is dissonant against the bass line. I wish I had spent more time playing the melodies, but I haven't. I was always more concerned about seeing that I was good to play gigs and just get through the bass part. I've done ok.
The bass line can't just be arpeggios, of course. To that end I learned to use scale steps to walk around through the changes when it was convenient (actually I've been able to find changes I had forgotten by walking on the steps). Sometimes, when it was ok I've been able to jump around a bit, only as long as the tune would allow. But, I've tried to not get stuck within just one octave all the time for the rest of the tune. At other times I've even found it useful to hit the root twice before going to the next note. Stuff like this has been very interesting to evaluate as I try to see what sounds good, or, on the other hand, to know what not to do again. Ya gotta try stuff.
I've never been one to use methods, though. Can't comment on any, but I'm sure there are good ones. I was fortunate in that I already knew theory, so I was able to figure a lot out by myself. But, today, I don't really consider myself a jazz player. I didn't delve far enough, but was taken by other styles, although I still like to play some standards when I get a chance. I'd never make it at a jam, though, unless they just happened to be playing the tunes I know.
Take notes at the jam and learn those songs that are the most commonly known. Then, get a chart and read it, trying different approaches, as listed above. Try not to be daunted by the other players when you get back to the jam. The more you play and learn, the more confidence you'll get over time. Good luck with it.