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Since you didn’t mention it, I assume that you didn’t have the A of spade. I can see bluffing if you had that card.
What hands would we shove for value on this river? AK, KQ, KJ, AsXs, JsTs, QQ. But I don’t think we would use the bet/bet/bet line with all of them.
What hands does BB call/call/check with? Possibly Kx, 9x, 88, 77, 66, 55, 44, JsTs, JdTd, QdTd, QdJd. Of these, BB may call a shove with Kx, JsTs, JdTd, QdTd, QdJd.
Some possible traps are K9, 99, AsXs. We would usually see a lead or raise at some point but some players like to be tricky.
I think I would check and take the marginal showdown value. You likely lose but still have a playable stack.