Thanks all for your helpful replies,

Everytime I really don't intend to worry that much about bouncing, I just say to myself, when it starts to trot I will be fine and fixed in the saddle, however at the first second of starting trot I found myself bouncing off the saddle, the weird thing is that I succeeded to make a two-point position in my trot, but that was against the pace of the lesson.

Is it real that the horse start to trot and I stay in the saddle? I began to feel it's like a dream

What can really prevents me from bouncing in the very beginning of the trot, if this happened and i succeeded in bringing myself fixed for few seconds then I am sure I will get the sense.

Is it thigh muscles? lower legs squeeze? or what else that I can try in my next lesson that would keep me on the saddle without bouncing?