I would be content with just writing out the bass clef with the chords written above each bar (ie as letters) for clarity.
not quite what you asked but also:
a simple version of C Am F and G would "walk" between them, outlining each bar's chord so as a simple on the beat line
bar 1: C E G B(up)
bar 2: (down) A C G E (down)
bar 3: (up) F A C F (up)
bar 4: (up) G F D B(down)
note that each final quarter note is just one scale tone away (harmonically and in pitch) from the start of the next bar so it "walks around".
I failed to answer one question of yours; you can use any note from the chord in your bassline, however be aware that some will sound better than others and affect the way the whole chord sounds (this is taking you into the realm of inversions). If you know a pianist or guitarist or can play guitar yourself, record a simple version of the chords and experiment with putting different notes in the bass under each chord.