Because Toph got gipped.
She could tell from the outraged muffled shrieks that Zuko was quite unhappy with her. In fact, she'd rather planned for it. She knew he wouldn't dare firebend at her again, not since the incident at the Western Air Temple, and therefore felt quite unthreatened when he mimed various katas at her with the limited scope of his hands. Tied up as they were, it wasn't getting him very far. She had a feeling he felt he hardly needed to be muffled, but the trip was going to be long and this time, he was going to listen to her sob story and like it. She tipped him unceremoniously into Appa's saddle and proceeded to shimmy up into it as gracefully as possible for a blind thirteen-year-old girl. Eventually, once they got far enough from the Fire Lord's palace to avoid a scene, she would have to untie her captive and let him fly the sky bison to a more specific location. For now, she merely hoped the creature would be clever enough to fly up and away from the guards who could shoot large fireballs from their fists. And Aang. He probably wouldn't be too impressed with the mysterious disappearance of his familiar.
"Yip yip." She exclaimed, barely containing a whoop of excitement as Appa leapt into the air and flew through the night sky. Zuko continued to bray muffled curses and obscenities at her through his gag. But Toph was determined. One way or another, she was getting her field trip.
Shortest thing I've ever written, but I needed to get her out of my system. Hope you were amused.