Welcome. I still do both. There are lots of us here.
Someone once said "you're never more than a half step [one fret] a good note." The problem is whether to go up or down, of course.
Turn on the radio and play along through everything - the commercials, etc. Develop that ear. It's the three minute challenge. Learn the song as well as you can before the DJ throws another song at you. Hint: The most common keys in pop music are C, A, G, E and D.
Pick and album and try to learn it all the way through, day after day. Go through another album.
I'm not a reader, but it would make my life easier if I were. Consider learning to read - there's a lifetime's worth material out there.
Respect the root. When the chord changes it usually the right thing to do to hit the root on the chord change.
"Be the player you want to be". When confronted with a song, imagine what "a cool bass player" would play and try to find it. When I started doing this I played a lot fewer notes and everything breathed a lot better.
I'm laying this out in black-and-white while acknowledging that I am glossing over a ton of stuff.
To me, the chord progression is the best place to start. Within any chord there are strong notes and weak notes.
Strong notes sound confident but aren't as interesting harmonically. They provide a solid foundation to the music but don't really spice it up as much. Weak notes have the possibility to make things interesting or they can just sound weak. They're more dangerous, but potentially more fulfilling. No guts, no glory.
There are strong places rhythmically to place them, It's generally a good idea to play the root when the chord changes to define the chord change for the listener. Generally it's a good idea to play a strong note on a down beat (one and three in 4/4 time). Other places rhythmically you have a responsibility to fill in with other tones to make it interesting to yourself, your band and your audience.
Usually the strongest notes in a chord are the root, the fifth and dominant seventh. You can make whole bass parts using just those notes over the chord and sound passible. You could be in a band that tours the world with just those tones. They will give you the most bang for the buck. Even when you branch out and move to more interesting tones, these notes will be prominent in your playing.
The next strongest notes are chord tones, the third and the sixth. These are dangerous because you are committing to a major or minor tonality and it sounds awful if you get it wrong. The chord tones are used a lot in jazz and blues but not as often in rock. I'll put the major seventh in this category. Dominant seven chords are more common and I put them in the "strong tones" category. If there's a major seven chord, I'd say it's a chord tone.
Next up come the scale tones, the second and the fourth. Both of these are safe in terms of tonality of the scale, the fourth is "perfect" there are no majors or minors. By second I mean major second - two frets up. A minor second, one fret up, is more chromatic to me. The scale tones usually want to lead your ear to the next chord or they're used in passing, on your way to a stronger tone. To reiterate, you are safe using the second and the fourth with either a major or minor chord because these tones are inside the scale but not in the chord - you aren't committing to a major or minor tonality. The second is more iffy with a minor chord because it's a half step from the minor third chord tone, the fourth is more iffy with a major chord because it's a half step from the major third. I think these are also known as "avoid tones".
Chromatic tones are the weakest. Minor seconds, the "wrong" third and sixth (and seventh) for the chord and the tri-tone. They are used when you are just passing through or perhaps the key is modulating. They are useful in chord substitions when you want to add spice, but if you don't pull it off they sound like a mistake. Use them with caution.
As with all music theory, this is just a general guideline - rules that have been successfully broken hundreds or thousands of times. But if you're in an unfamiliar situation and either for your own sake or for the sake of the people on the bandstand with you or for the audience, work more in the "strong tones" area and things will at least be firm. As everyone gets more confident start branching into the more interesting tones.
Typical fingerings of intervals:
Root: the named chord - A in an A, Am, A7, etc. It's octave is two strings and two frets up.
Minor second: One fret up from the root (or two strings and one fret down in pitch).
Major second: Two frets up from the root (or two strings down in pitch and the same fret).
Minor third: Three frets up from the root or one string up and two frets down in pitch.
Major third: One string up and one fret down in pitch.
Perfect fourth: Up one string on the same fret or one string down and two frets down.
Tritone (aka augmented fourth or diminished fifth): One string up and one fret up or one string down and one fret down.
Perfect fifth: Up one string and two frets or down one string, same fret.
Minor sixth: Up two strings and down two frets or down one string and up one fret.
Major sixth: Up two strings down one fret or down one string and up two frets.
Dominant (minor) seventh: Up two strings, same fret or same string, down two frets.
Major seventh: Up two strings and one fret or same string, down one fret.
Over three strings you have two easy places to get the root, the fifth and the dominant seventh:
Root and it's octave up: Up two strings and up two frets.
Fifth: One string and two frets up or same fret one string down.
Major seventh: Two strings up same fret or two frets down same string.
So using octaves you have six very solid notes at your disposal in very close proximity.
All of this is to encourage you to branch out, but if you want to get things going quickly, that's one way to do it.
KO