My guess is that while she mounted a flying lizard, she is not yet able to control said flying lizard. Hence, enter Tyrion to do what a lot of people think he is capable of doing...
we're named Dragon Trainer, while previous books had his chapters named Tyrion. It's obviously his destiny. One of the first scenes has him reading a book on dragons by the camp fire. The saddle he made for Bran, was from that book.