Shillx, are we really afraid of the straight here? Would BB 3-bet PF with 98, 43, or 83? It seems like AK, A7-A5 or 77-55 are the culprits here ... maybe even your A8 hand. (Tough to 3 bet the field OOP with 77-55 though, no?)

If we're afraid of these, why not raise the turn here to test the waters?

Worst-case is that BB 3-bets the turn, we call for the straight & fold to a bet if we miss assuming the baby set or better A-kicker. But, in this case, we're no worse off than the hand as you've laid it out.

We could win if the villain has KK, QQ.

We could earn a call on the turn & check on the river (which we could take or not), saving a bet if we're beat.

No?