Composing a bass line isn't mystical. It's a four-step process you can follow on any song with chord changes.
Step 1: identify the chord progression and tempo
Get the chord chart. Figure out the BPM (use a metronome or a song-tempo finder). Note the key.
Example: a song in A minor at 90 BPM, progression Am - F - C - G (the i-VI-III-VII, very common in rock).
Step 2: roots, locked to kick
First draft: play the root of each chord, one per beat, on whichever string puts it lowest in your range.
beat: 1 2 3 4
Am: A A A A
F: F F F F
C: C C C C
G: G G G G
This already grooves. Play it for a verse; listen.
Step 3: add an eighth-note movement
Pick a sub-rhythm. Common: every other beat is doubled to an eighth note.
beat: 1 & 2 3 & 4
Am: A A A A A A
That's just sixteenths but you only play on certain hits. Now the line breathes.
Step 4: add a fill or walk between chords
The last bar of each chord transitions to the next. Use a passing tone:
Am - F transition: ... A - G - F (walks down from A to F)
F - C transition: ... F - E - D - C (walks down from F to C)
C - G transition: ... C - B - A - G (walks down)
G - Am transition: ... G - A (steps up by one whole step)
The "walk" notes (G, E, B, A in the examples above) connect the chord changes. They make the bass feel melodic, not just rhythmic.
Practice
Pick a real song. Identify the chord progression. Apply the four steps. Record yourself playing the bass over a backing track or just over the original (turn the original way down so you can hear yourself).
Iterate. Try different sub-rhythms. Try sparser fills, then busier ones. Find what fits.
When in doubt: less
A composed line that breathes is better than one that's busy. Listen to Billie Jean (Louis Johnson). The line is sparse, mostly roots, one walk at the end of each section. That's a memorable bass line.
Next: 5-string basses and beyond.