It also helps to listen to different types of music. Don't just listen to rock. listen to some jazz, funk, latin. You'll start learning how to impart a different texture to songs. I sometimes use the mixtures of Latin and walking bass lines in sections of songs or in fills, but wouldn't be able to if all I knew was eigth-notes on the root. Remember, the bass adds the texture, the "feel", the mood, to the music. Explore.
I actually listen to a lot of jazz and funk, I just don't feel competent enough to apply any of the stuff I learn from it
I have the opposite problem. I can come up with a tricky/catchy bassline no problem, but coming up with the rest of a song is very difficult for me.
Have you tried to "write" or jam collectively on ideas? That's how my band approaches writing 'our' songs. BL/songwriter comes in with an idea-- usually he has the words and basic form of a song down. He might have something in mind as far as parts for the other musicians, but in general we just make up parts and play along until we all like what we're hearing. That's the song written.
Technically we do, problem is none of them play bass and the only one who could help me (drummer) is lazy and doesn't participate when we're writing songs
Rythmically and melodically you want to complement the melody (counterpoint!), and harmonically outline the chord changes and avoid parallel fifths (half joking here, for the theory nerds, but seriously).
For rock, lay into the back beat, i.e. lock with the drum part, emphasizing roots and fifths on the dominant beats, which frees you to play any kind of passing notes/runs/fills in between.
For my money, learning and practicing arpeggios (major, minor, augmented, diminished, half diminished, with major/dom 7ths, all inversions) is critical. Scales are important of course, but don't sleep on arpeggios as fundamental building blocks for bass lines.
I originally came up with the song doing arpeggios on my bass, but then I turned that into the guitar part and screwed myself over because I didn't want both guitars and the bass all doing the same which has now led to this predicament