Hello Stu,
I guess "bouncing" refers to some explosive or plyometric (i. e. a excentric muscle contraction immediately followed by a concentric contraction) movements shown in some of the videos.
Whether these movements are appropriate or not depends on the goals you want to achieve. If you are training for sport- or occupation-specific tasks and these involve fast movements, you´re better off to practise fast movements now and then.
You are not supposed to do bouncing movements (except to complete the last set of a given exercise :-)) in traditional strength training, which is based on the idea that you aim to isolate the muscles you train.
Things change when you do complex exercises like cleans, snatches, jerks or deadlifts, where bouncing movements are sometimes required to preload some muscles and to accelerate the weight you are trying to lift.
Suspension Training consists of complex exercises, since you never train only a single muscle, but always chains or loops of muscles which transfer force from the feet you stand on to your hands that hold the handles of the TRX.
Bottom line: Bouncing movements are ok as long as you are aware of them and do them by design. You don´t have to do them but depending on your goals they might be a useful variation.
Hope that helps,
Olaf