Alright, Kaycey.. Here I go. XD
You did great, he seems pretty quick, as you described. Obviously not the smoothest ride- I can relate.
Bring your lower leg leg back so you have more contact with him, and just squeeze him instead of kicking him over and over. I don't know Cowboy, so that might not work for him, but it will save you from bouncing around, too, if your squeezing yourself to him. Okay, that sounded.. weird..
You might wanna try to bring your foot forward in the stirrup a little bit.. Might wanna try to do no stirrups at home so your stronger for lessons?