gigemaggs99...the following assumes that you are using clip-in pedals. If not, it won't help you. Also, I am not a coach, just another guy who had a similar reaction when I started working on cadence drills.
The first few times that I tried to push my cadence up and go for longer than about a minute, I noticed that towards the end of the interval I was bouncing around in the saddle like a superball. I had heard that one factor that can result in bouncing in the saddle is if you have your seat too high, forcing you to rock your hips almost like you are trying to waddle in the saddle. So I dutifully lowered my seat only to find that I still bounced when I tried to push at a higher cadence over the course of several minutes.
After studying it a bit, I found that I was bouncing because I was only mashing down on the pedals. Each downward mash would force my opposite hip to raise out of the saddle just a bit. With the next mash on the other side of the bike, the other hip would raise out of the saddle. It was simply a cause and effect condition of being a serial pedal masher. You do that a few times really fast and you will definitely be bouncing, and probably be unable to push to a higher cadence. At least that seems to be the way that it has always worked with me.
The main thing that I focus on now during Fastpedal is to pull through the backside of each pedal stroke, not just mash down on the pedals in the front half of the stroke. When I concentrate on pulling through the backside or upward portion of each stroke, my cadence rhythm improves dramatically and I can get a ton more rpms without any bouncing in the saddle. To the contrary, when I pull hard through each stroke, it's like I am bondo'd to my saddle. For me the effort of pulling through the back half of each pedal stroke keeps me anchored properly in a counterbalance to the forward push that I am giving on the opposite pedal. Once I get in that smooth rhythm, my cadence shoots up, and I don't bounce unless I start getting sloppy or tired.
Hope this helps. Keep working the training program. It works!