If you have a good riding school the instructor should explain that the trot is a 2 time gait where the horses legs move in diagonal pairs.

Before you set off to ride do see that your leathers are the correct length for you because if they are to long you will ride on tip toe and if to short you will tip forward and bounce.

Do see that you have a supple back and seat moving with your horse and a nice long relaxed leg from your hip,see that you are sitting up right with your tummy facing forward and having dropped your shoulders to give you supple arms and elbows through to your wrist and fingers so that you can allow your horse to go forward..if you are supple through your back and seat you will feel your horse moving under your seat.

Whilst walking on your horse let your leg come down from your hip and look down and you will see the tip of your toe just in front of your knee.
have your leg around your horse but with no gripping because as soon as you grip this will send you away from the back of your horse and out of balance.

when your horse is walking nicely forward ask for trot as he starts to trot keep your leg long and underneath you your knee and ankle become a spring
for your up and down movement, no gripping its a little like standing up and down in your stirrups but you only need to rise a little not right up into the air
the movement of the horse will help you to rise as he changes diaginal prs of legs this gives you a 2 time movement ,as you rise your tummy is moved towards the horses ears and you can count to your self 1,2,1,2,1,2 .
if you need to use leg aids to keep the horse trotting apply a little sqeeze of your lower leg as you come down to sit in the trot not on the up of the trot.

It feels like you are springing up from your ankle do try to keep your lower leg long and underneath you and not shooting forward or back.

Whilst in rising trot you do not need to grip with your thigh or lower leg just have your leg around your horse if you grip this makes you stiff in your legs and upper body and you will then bounce away from your horse hence bouncing.

Also when you are learning to trot only do about 10 strides as the longer you go the worse it feels if you have lost the flow and then try again for another 10 strides.

In time you may feel in tune with the horse for only a few strides but once you have have a few nice srides you know the difference and the rising trot will come with practise and suppleness and balance as you improve.

It is very easy to say no gripping its the first thing a novice rider does to feel safe and they think gripping will keep them on ,,it does not gripping pushes you away from the horse to move with the horse is what you are aiming for.
ask you instructor teach you about riding on the correct diaginal this is important for the comfort of the rider and the horse and for the transition to canter and more.

best wishes to you .