I think I would take my chance right here, even with the Ace on the board. Chances are BigStack would have raised with an Ace. SB might have had one, but not wanted to play a big pot on bubble. There's always a risk when an Ace hits the board. We know a lot of players simply won't fold an Ace. But just because an Ace hits the board doesn't mean someone has one in their hand.
I'd take the chance. If blinds are going up next hand (presumably 4000/8000), you're going to be putting another 4k in the pot with who knows what. If you complete, you'll only have 6k behind. So you would be pretty much committed. If you folded the SB then you're left with 10k and have 5 hands to find something to shove with before you're back in the blinds again.
Option B is to try to fold your way into the money. I'm assuming, however, that you are the short stack (you didn't say), in which case, all the rest of the table has to do is wait you out. With an M value of just over 1 (don't know what ante is), they won't have to wait long. Again, I'd take the shot in the hopes of winning, as opposed to waiting for someone else to lose. If you were to get blinded off, or get your chips in another spot and lose, you're going to think back to this hand and wish you would have taken the shot. I'd go for it.