Bouncing can happen at any fitness level. Not working on it only reinforces it so the OP is taking a good approach in trying to fix it now instead of in 10 or 20 years.
Saddle position does affect max rpm but shouldn't affect smooth pedal stroke, not at the normal cadence ranges of 100-120 rpm. A lot of set back, too high of a position, or even slightly too low, these will increase the chances of bouncing. Higher speed pedaling will reveal pedaling form weaknesses so try doing extremely high rpm drills to work on form.
Focus on "spinning faster" instead of "pedaling harder". I tell people not to think about scraping mud off your shoe - that's fine at lower rpms but at higher ones it's too much. Just move your ankles in circles really fast and let your foot just follow along. You can stiffen up your ankle if you want, keeping your foot at a somewhat standard angle, or you can let your ankle flex and therefore your foot to tilt at the different parts of the pedal stroke. I do both at different time - for max rpm (highest cadence) it's more a stiff ankle but for my best sprints (highest speed) it's always been more of a flexy ankle.
Try going to very extreme pedal speeds (for me I do it on a trainer or on a spin bike, the latter with the seat lower than I have it on my bike). The idea is if you can pedal at 240 rpm then 120 rpm should feel pretty manageable. In fact if you spin up a few times you'll find yourself lowballing your cadence by a good 10-20 rpm, meaning you do a couple 200+ rpm bursts and then "recover" at 100 rpm only to see that you're doing 120 or higher. On my road bike I have a hard time breaking 220 rpm at my regular saddle height, but that height is optimized for a lot of stuff, not just max cadence.
Do whatever you need to do to smooth yourself out, even if it's a temporary thing/tactic. For example when I started riding a lot I bounced too. I found that holding my upper body totally rigid really helped. It wasn't practical in terms of riding efficiency but it forced me to figure out how to move my legs without moving my upper body. Many years later a rider commented on my "still" upper body - it comes from those drills at the beginning (and for those that ride/race with me I'll admit that I exaggerate my upper body movement to try and broadcast what I want to broadcast, so it may not be a reflection of my true pedal form).
You can even (temporarily or permanently) lower your saddle a bit. A tip - if you've tilted your saddle down more than a couple mm back to front (so the nose is a couple mm lower) then your saddle is definitely too high. Level or almost-level your saddle, drop it, and work on your form. My saddle runs a couple mm lower up front, and based on the hoopla that happened when the UCI started checking TT bike saddle "levelness" apparently most of the pros do too.
Another thing I did was to go out and do "rpm rides". Back then I could average 95-100 rpm for a ride (using the average cadence function). I set out to do 120 rpm for at least an hour. That translates to a lot of 125-130 rpm riding because the average really gets affected by the brief periods of lower rpms (just like your car's computed avg speed of, say, 65 mph, is usually 10 mph below your actual driving speeds because to average 65, even on a highway trip, you need to hold 75 for much of it). I only managed this a few times over the years but simply trying to hit it and failing after doing 120 rpm for 30 minutes, that's better than not doing 120 rpm for 30 minutes. A tip - if I was riding outside I found that I was in my lowest gears for most of the ride and I had to avoid hills else my average would drop dramatically.
Rollers are great for those avg rpm rides, ditto a mag trainer. Exponential resistance trainers (fluid, wind) tend to force you to use low gears which in turn give you low wheel momentum so the ride is much more choppy (and unrealistic). Your wheel slows down quickly during the top/bottom of the stroke so you end up with more peaky type pedaling. It's sort of like spinning up a hill vs spinning on a flat road.
The most important thing is to fix your bounce now. Don't let it go, thinking you'll fix it in the off season. I have a good friend who did that and he rues it to this day, over 25 years later - he cannot get rid of a significant bounce in his pedaling form.
As far as optimal rpm it of course depends on the rider. Longer cranks drop it, shorter ones raise it. On 175s I'm a 95 rpm kind of guy. On 170s it's more like 110 rpm (meaning what I spin at when I'm feeling comfortable and fresh). My actual averages are about 10-15 rpm lower than that so my avg cadence on 175s is usually in the 80-85 rpm range, 170s is 95-100.
My spin bike drills (at the beginning). On the track (170s) I don't think I exceeded 125 rpm since I only went about 32 mph in a 50x15. On the spin bike I could hit 244 rpm (and that was on 175s). On 170s on the same kind of machine my max rpm was over 280 rpm.