What I try to do is emphasize the bass notes in the chord that I'm playing. When the singing stops at the end of a phrase, I try to fill with a musical idea.

A good strong bass-chord style will carry you a long way.

Flat picking seems to do this easier than finger picking. Although Burl Ives did just fine with a bass note with the thumb and a chord plunk with three fingers.

You can play faster accompaniments with a flat pick by picking down on a bass note and up (cross picking) on the chord.

Sometimes, just strumming down on the chord on the beat is good enough.

A few tasteful bass runs create interest also.

Hope I helped some.

Frank