Loluores: Been thinking about your question (and how best to answer it well )...
I'm not a keyboardist but primarily a pianist (in fact, a classical pianist sef, not even gospel or jazz etc), so I don't really play in that style so much these days, using the LH to play bass only. I'll try to do justice to your question though
What I can say is, try to use your LH to emulate the way a world-class bass guitarist would sound in whichever style of music you're interested in
Some tips:
One thing about bass is that it incorporates RHYTHM as well as the progression or bass line. So don't just use one finger to hit one note, make it rhythmic
Also, as you mentioned, use the cycle of 4ths/5ths frequently (many progressions utilise this). If you have a target note, like fah for instance, you can quickly play s-d then land in fah
Use tritone substitutes occasionally e.g. instead of r-s-d you play r-de-d (or r-s-de-d), t-m-l becomes t-ta-l (or t-m-ta-l)... especially if the harmony suggests it e.g. when playing altered dominant 7ths. Veeeery jazzy, handle with care
If you're hitting one single note in several bars, like a constant doh for example (in music theory this is called a pedal point or a 'basso ostinato'), you can vary it a lil'. By adding the dominant note (soh) in-between, making it rhythmic also depending on the style of the music
In modern gospel, the PENTATONIC scale is used a lot in bass progressions. Again, if you're hitting one constant bass note like doh, you can do stuff like d-s-l-d.... d-l-s-d... d-s-l-s-d... d-re-m-s-l-d
You can always go CHROMATICALLY into a target bass noten either from above or below: d (r-re-m) f (l-ta-t) d is a typical up-tempo gospel progression
Consider this progression from the Jackson-5 (yep, I'm very old school ) in 'I Want You Back'
d..r-m-s-l-f..r-m-f-fe-s-se-l - m - f - d..r - s - d
Here's the breakdown:
d
r-m-s-l (pentatonic scale on doh)
f
r-m-f-fe-s-se (diatonic (r-m-f), then chromatically going to the target note lah)
l-m-f-d (fourths intervals l-m and f-d)
r-s-d. (2-5-1)
Don't forget the rhythm of this progression as well as the notes. This goes for any bass line you play in any style, let your LH feel the rhythm and play it as such.
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