Speeding up 101: Use a safe and controlled environment like the round pen.
Confidence building 101: Move closer, stay longer. If speeding up makes you nervous, do a lot of what you are confident with and a little of what makes you nervous. Get as close as you can to your goal and stay as long as you can. When the nerves become to much, go back to what you are comfortable with.
Here, Cordelia gets as close as she can to her goal of trotting with two hands on the reins - one hand on the rein, the other on the saddle horn. Together, we get Shorty to jog circles for as long as she is comfortable with. Next, we will take a break, take deep breaths and pet him all over. Whenever she is ready, we return to gaining confidence and balance at the trot.