I don't think you can profitably call this river. You have shown strength by betting 3 streets and I doubt he is shoving over your river bet with anything worse than two-pair. That being said I think c/c up to maybe a 2/3 pot sized bet on the river is a better line than betting it. Your hand is pretty much a bluff-catcher by the river, and I don't see any point to make it a bluff on the river.

As a side: Is it just me or is BB's line in this hand completely retarded for pretty much anything he can have here? I mean a solid player will not take this line for value with anything less than two-pair really, and of those hands a nut flush is pretty much the only one that I could see a good player calling two-streets with. Even then I would think he would at least raise the flop or the turn. Of course, at this level, I expect to see slowplayed flushes and sets much more often here than I would expect to see bluffs, but am I the only one who would be tempted to call this river against a thinking aggressive player?