does anyone have any advice for me to get my electric bass to produce a jazzier type of tone?
"sex" is not the answer, "Sex" is the question, the answer is "yes"
Try changing the pickups... I'm not sure what pickups would provide you with this tone, but I'm sure someone else will know.
uhm, i think the real first question should be "What kind of bass is it?"
Its better to regret the things you did, rather than the things you didnt do.
An easy step to a jazz sound would be putting flatwound strings on your bass.
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I used to have no problem at all with this till I traded my fretless, passive single coil, flatwound strung Yamaha for a fretted, hyper active humbucker/singlecoil pick-upped, round wound strung Ibanez. No matter what I tried; it would rip apart any music exept the hardest of rock. Quite frustrating, since the beast cost me a lot and I don't actually play that much hard rock.

But after some experimenting I came up with a decent mellow jazz-tone. First I raised the action a bit. I switch off all pick-ups exept a single row nearest to the fretboard, put the tone knobs on medium and dial in a clean sound on the amp, with the gain knob on absolutely zero. Then I pluck above the fretboard with a smooth, rolling motion of the fingertips. The fretting I do with a sliding motion that meets the plucking in one and the same moment (the plucking starting a fraction before the string is fully fretted. That is where the higher action is for; to give a wider time frame to do it) It takes some practising to get the smoothness and coordination right. I'm still working on it, but I'm getting there.

As said, it all depents on your equipment. You won't easily beat a fretless with flat wounds in this, and never a proper acoustic upright.
^^Good job Marcel. Saved me alot of time.

To get a good jazz tone, put your bass tones at about 8, mids around half, and highs anywhere between 3 and 7 (depends on what sound you want. I prefer them around 6 or 7).

Now on your bass (assuming you have dual single coils), take the volume for the bridge pickup and turn it all the way down, leaving the neck position wide open. Play off it and pluck lightly.

Now if you want a Jaco type sound play off your bridge pickup, with the volume cut on the neck, boost the mids, and cut the lows. That's the closest you'll get without a fretless.
instead of playing with your finger right in the center of the fret put your finger right on the fretbar, it will give you a little bit more of a fretless tone, also like others have said play right off the bridge, boost the bridge pickup, if you have any eq on your bass, max out everything and then adjust as necessary on your amp.
"music is a unison of emotion and technicality. without technicality you have chaos, without emotion you have sand"