On the river with the nuts it really comes down to a math problem. How often do you think the villain will call this bet? What about a PSB? What about a 1/2 pot bet? It is hard to say what the best play here is without a read on what the villain will call. Readless I would probably just bet $10ish on the river, your line seems a lot like a flush [check/call with draw, lead turn when flush hits] by pushing you are really only getting called by a full house or ace-high, maybe king-high flushes neither of which seem all that likely, but I guess are still possible.

There is a chapter in NLHE:TAP about how much to bet on the river with the nuts, its good reading, you should check that out.