The trap is set by creating a negative pressure within the bladder in comparison to the surrounding water. The trap door has trigger hairs that are tiny little levers that hold it closed. When the prey brushes against it, the trigger hairs move and the trap springs open, which sucks in the water and the prey, then the trap door closes; all within 15 milliseconds.
The plant bladder pumps water out of the bladder via a mechanism called Active Transport, which you can read all about in Wikipedia. This basically pushes water out of the bladder via the membrane, thus causing the negative pressure, which allows the trap to be set. All very cool!
This is one plant that engineers could get excited about!