Why don't we play her AP?
All of her spells scale off AP (and a bit of AD for E), they all deal magic damages (E's passive is magic & active is physic).
Well some of the ADC items suit her way better than AP especially canon or Runaas but well, considering her ratios & type of damages that's a shame. 
Damage from her E is gated by basic attacks. This restriction somewhat homogenizes the gameplay between an AD- and AP-focused build by requiring her to land 4 basic attacks for maximum damage in a single rotation. Prior to her update, she could build AP and instagib people simply by jumping in and pressing E+R. Nowadays its not so simple.
Trist used to be fairly viable as an AP assassin, but since her rework it's not really a thing. Goomba stomping puts her in an awfully bad situation unless she can make the target go away immediately, but her e is no good for that and her ult isn't going to be enough to kill someone.
Oh the days of the AP Tristana one shot
AP Trist was a fairly toxic playstyle, so Riot nerfed the shit out of it in her rework.
They gutted AP Tristana for very good reasons.
