Bubble time: Weak Ace all-in on A hi flop, bad play or bad luck?

[McMelchior]

PStars NLHE $10+1 rebuy, 169 starters, down to 23, money for 18. Level 12, Blinds/ante 2k/1k/100.

I have 32k after posting the SB, BB has twice as much, average is 39k. I was recently moved to this table and have no read on BB, but this is a low buy-in PStars tourney, and by far the most players are very loose and fairly aggressive.

Folded to me on SB, I raise to 6k with A6, BB calls.

Flop Ad Kh 5d.

I believe the BB to be able to call with any kind of hand, considering his stack size, and decide not to risk a free card. I pet the pot, 12k, leaving me with 15k.

Should this have been an all-in, considering I'm commiting 45% of my stack and are not going to lay down to a re-raise? I'm split on the issue, having seen all-in's once in a while gettting less respect than pot-size bets?

Anyway, I'm re-raise, push the last 5k in, and lose to an A7.

Bad play or just bad luck?

There's 12 minutes to the next blind increase, but with a cost of 3,900 per round I don't think I could have folded my way to the money, and making $60 wouldn't be that interesting anyway; even though I think the BB would have called with all but the most hopeless hands I can't see myself checking of folding PF.
And honestly - after BB's PF flat call, could I have check/folded that hand on the flop? Am I doomed to make this a coinflip for all my chips against any Ace the BB could be holding in this situation (assuming he would re-raise PF with AJ or better, leaving him to call with 4 Aces worse than mine and 4 better), or is there a different way to play this?

Best,

McMelchior (Johan)