Annoying bounce

It could be saddle height but the most likely culprit is an inefficient pedal stroke at high RPMs.  Everyone will bounce at a certain high cadence because you won't be able to efficiently spin in circles.

You're pushing and pulling on the pedals at imprecise times at a high cadence as opposed to spinning in a more "perfect" circle.

1. Concentrate on spinning in a circle.

2. Why are you worried so much about high cadence riding?

Yeah, it makes sense, mostly because your bike fit is bad.  100-110 isn't that high of a cadence.  You should easily be able to do that with little resistance on a trainer. 

Try relaxing the calves. Think of moving your ankles in little circles. Don't ever think "pedal harder", think "pedal faster". And engaging the core, as already suggested.

You also might try just a touch more resistance as well.  If I have a bit of bounce with the higher cadence, adding a bit more load seems to smooth this out for me.

Adding resistance just slows down the cadence and that's why the bouncing starts to disappear.

The whole reason for the bounce is that your leg is still pushing down when your pedal is at the bottom of the stroke -- since the pedal can't go any further down, your body goes up. It's a direct result of your muscles wanting to mash the pedals rather than moving your feet in a circle. It's not an automatic thing, it takes time. Working on it directly (one-legged drills, working on relaxation of the lower leg, building cadence slowly) will lessen that time, but it will still take time.

If you just keep riding a lot, and varying your cadence as you ride, you really shouldn't have to think about it too much.  It will become natural as you 'just push'.  Because your feet are 'locked in', they are going to move in the 'correct' fashion.  Eventually, the muscles in your legs will learn to fire in a more efficient pattern to allow this to happen without 'bouncing' (assuming your seat is not too high/low, etc.).

Cycling???

Three things potentially at play here:

1) The shoes are too tight or are strapped too tight

2) Cleat position isn't where it should be

3) You might have some imbalance on that side that may need a varus/valgus adjustment (shim) to the shoe or cleat