I can't tell you the ideal play, but I can tell you my recent experience.

4 times today, I was in the basic position you describe. The first time, I had an Ace came on the flop and faced just the BB. I bet the flop, he called. Bet/called the turn. I bet the river, and he folded. I don't know what he had, but I'm guessing either nothing, or low pair. I had King high.

The next three hands were similar, except I checked the river. 1 person bet back at me and I folded, and the other two checked through. I lost all three of these hands.

I have to wonder, had I bet the river, could I have gotten one of these three to fold? If so, wouldn't this be the best play?

I wonder out of ten average players, how many would fold the river with a low pair facing a bet to them?