Unfortunately I think Barriss heartlessly picked Ahsoka because she was her friend and Barriss knew she could control Ahsoka. See "Brain Invaders" where Barriss is the leader between two of them. Picking Ahsoka was honestly one of her big mistakes, along with thinking hitting Ventress with a pipe was enough to kill her, and not tossing the red lightsabers out. I actually don't think Palpatine had much to do with Barriss's scheme to bomb the Jedi Temple. The episode is much stronger without his direct involvement. I think Barriss acted on her own with a violence meets violence philosophy trying to protest in that way much the same as the picketers early the the episode. This is because she sees the Jedi as fallen heroes and nothing more the Senate's living weapons leading their destructive armies. She framed Ahsoka to take the fall and to create a great divide between regular joes, the Senate, and the Jedi themselves. The sad look of regret in her eyes is because of what she did to Ahsoka among other things.