Not really sure I grasp the question, but...
Have you thought in terms of developing a bassline that acts somewhat as counterpoint to the melody? Sort of a "subterranean melody" that 1) provides some harmonic contrast to the main melody, 2) carries the basic rhythmic "feel" of the song, 3) hits enough of the root in all the right places to function as a genuine bassline, yet 4) can more or less stand on its own as an independent "sub-melody".
As far as the particular sub-melody you choose, that's a matter of inspiration & creativity - as usual. You're on your own there...
Some of McCartney's best work with The Beatles would do that. So would some of Chris Squire's best work with Yes. Ultimately it all goes back to
JS Bach - regardless of the genre you favor...
MM
