I don't know about the bike fit you received. There is the quick, ballpark type fit which pretty much involved a bike person "eyeballing" you riding position (Is the seat high enough? Do you look comfortable on the bike? - good enough). Quality of such a fit is dependent on the diligence and education of the fitter. Then there is the certified bike fit. This costs a tad more money and is usually worth every dime you paid. Consider the tens of thousand pedal strokes you will take over time. Imaging lower back pain with each stroke.

Here's a quick check you can use to determine if you are "in the ballpark" of a good fit. You can approximate good seat height by placing the heal of you shoe on the pedal in its lowest position. You should have a slight bend in the knee in this position. Also, with pedals at 3:00 and 9:00 positions, you should be able to drop a plumb line from the front of your kneecap through the pedal spindle.

One cause of bouncing at high cadence is low resistance. Try clicking up a gear or two. Consider smoother pedal stroke, as already mentioned.