Overall, I liked how you slowplayed it by checking on the turn when there was an A as I assume you were wanting to trap him if he makes a bet and you would either check-raise or smooth call him and get more money on the river.

However, you already indicated that you believed BB had at least an A, so why not lead with a modest size bet on the turn when the A appeared? BB would definitely at the very least call your bet and if he reraised you then you would have had a chance to re-evaluate if maybe instead he flopped trip-8's or was protecting his pair with AK. You should have also made a modest bet on the flop, as someone holding overcards such as an A would probably call to at least see one more card on the turn.

But regardless, you were going to be beaten on this hand no matter what you did with BB's pocket A's. Your trap was basically outtrapped by an even sneakier trap!

Regards, Steve