What do do with this draw on the bubble?

[curtains]

I agree with checking on the flop, with the intention of check raising. Unfortunately when it's bet AND raised to you, now you have a much tougher decision. I feel like folding is the correct choice due to the prize structure. If this was a winner take all tournament I would put my chips in and gamble, as you seriously have a powerhouse draw.

Once I was in your situation on the turn I would call the allin, and hope the shortstack loses, so you will at least get 3rd place anyway. By the way notice how bad it is to call for 2000 on the flop to just see one card (Which would be the case if you planned to fold on the turn). This is something you MUST avoid when you have such a draw, often by putting all your chips in on the flop, or simply folding if the pot odds don't look sufficient.