I learned this by asking a friend in the CouchSurfing meetup who brings a guitar or a roll-out piano. And as I say, I can't play any instrument myself.
Maybe if I want to learn, I should choose an instrument that uses single notes, it might be easier.
Regarding singing though, my ex-girlfriend told me to sing more quietly in church because it sounds so bad.
It's not just limited to bass/lead guitarists either - finger style acoustic guitarists don't play just chords. OK, often the fingerings are chord patterns, or arpeggiated chords, but that's not always the case. Checkout the title track from Bensusan's album, "Intuite", that is mostly just a single note melody: https://www.youtube.com/watch?v=di1qQsGcaIc (it would appear the ending is cut off this track here, but it gives you the idea).
I'd say the easiest / most immediately rewarding way is to pick up a guitar or similar (banjo / uke / banjolele / mandolin etc) and learn a few chords. Although people who can do that aren't exactly in demand so there's a case for learning the onde martineau or glass harmonica or something - that way if you get decent at it you can actually get paid to do it.