Sure, you can absolutely find many pieces, either for cello or double bass, that are "parts" of a larger piece but still sound like the piece overall. One of my warm-up pieces lately has been Greensleeves, for example, which is simple and everyone knows the tune, but I don't need accompaniment for it to sound enjoyable.
I mostly work with etudes, which of course are more solo-oriented, but I've spent some time on imslp finding some bass/cello pieces or parts, and there's a lot of it out there.
Playing music for oneself is of course a valid pursuit of playing an instrument. I'd argue that every musician plays their instrument, and practices, because they love the sound even when they're by themselves.