First of all, congratulations! It sounds as if you have a lovely young horse with free swinging paces.
As you say yourself, your horse is just broken in and still very green. He ought to be. He is only 4 years old. Still a baby. He will need about 3 more years to fully mature. That's physical maturity - mental maturity should follow that.....
Establishing your horse "in the basics" is your most important goal (right next to having a lot of fun TOGETHER - him too)
Falling out on a circle -
Yes, circle work is important - however, be sure you don't forget to get rhythm, relaxation, contact and impulsion first. With this you can ask for "straightness" (this is what you are after: Straightness on a circle, - a line where his hindlegs follow the path of the frontlegs)
Your horse must be going forward with relaxed and powerful strides first which you than guide into a circle by gently indicating the direction with your inside rein (take and give), allowing but guarding with your outside rein.
Remember that you merely "indicate and guide" with your reins. The main initiator to turn, however, is your body: Utilize your upper body by bringing your inside shoulder back which will also influence your pelvis/hip/leg position. The moment you only try to turn the horse's head and neck without also RIDING the turn yourself, you will make your horse fall out or become crooked elsewhere. In other words: Turn your horse onto the circle by using your whole "body attitude" to ride the circle not just the reins. And also remember that riding a perfect circle is a pretty difficult exercise for a young horse that is just establishing his basics and re-establishing his balance under a rider.
To help him by riding from point-to point is a good idea - but instead of four points, make it eight. Your horse (and you) will find it easier to stay balanced.
Never forget the training scale:
Rhythm - Relaxation - Contact - Impulsion - Straightness - Collection
Your circle work falls under "straightness" (as in "hind legs follow path of front legs"). See how important each step is in order to achieve the next?
And now we come to....
Sitting to a bouncy trot -
Since he is such a young horse and still needs to develop his carrying power and strength, I would not do too much sitting trot work yet. (But you know that)
Your problem is to sit to his trot, which is "bouncy" as you say.
A big, bouncy trot can become even harder to sit if the horse is not swinging over the back.
Re-read the training scale above and analyse if you have your horse working in a nice even rhythm, relaxing into a soft even contact? Is he happy to stretch down and out (long and low)? Do you feel he is picking you up, or is he hollowing under you - or just stiff?
If he is a big moving horse with a swinging back, your goal is to stay relaxed and soft as well.
This is not easy as "self-preservation" makes us to "resist" in order to absorb shock. But that also makes us stiff. And something stiff on something swingy will bounce off.....

So your aim is
a) to make sure your horse's back is not tense (see training scale)..... get him going relaxed, loose, and supple.
b) if a) is ok. and horse is swinging over the back, you need to relax and go with him with a supple, soft but toned body. Allow it to happen. Swing with him. Try not to "save" yourself, as you will automatically resist the movement..... which results in boucing...
To learn how "to let go" sometimes needs a little help: If your saddle has D rings, attach a small loop of bale twine as a so called "monkey grip". When practising your sitting trot, you can hook into the loop with your little fingers and help your body to learn to relax as you draw yourself into the saddle.
Longe lessons, no stirrups, developing your core-strength, breathing exercises..... all this will help you to get a better seat. Watching good riders and analysing the biomechanics also helps.
Good luck and happy training and riding.
(Don't forget to have some fun.... and make your training sessions interesting, so they never become boring work sessions...... -

C.