Always fold river against unknown?

[stickdude]

I think in this case I'm either folding the turn because it's still a relatively small pot or calling the river - both to find out what kinds of hands BB will do this with and because this will be a busted flush draw some percentage of the time.

The way you've played this it's pretty easy for BB to put you on two overcards, so he's going to keep firing even if he missed his flush.