The first time Toph rides Appa, she is exhilarated and apprehensive at the same time. She's leaving her overprotective parents—she's free to roam and earthbend and pick the dirt from her toenails as she pleases. Then Aang cries, "Yip yip!' and they're off.
The first time Toph rides Appa, she shivers and curls up into a fetal position, rocking back and forth, back and forth, until she just falls over from exhaustion. She doesn't sleep because she can't. Only Momo notices her distress and curls up beside her.
Later, she wants to be strong, but she blames Appa anyway.