It takes time (and training) to learn to spin a high cadence. What you're experiencing is natural for a new cyclist and most likely isn't related to bike fit at all.

To train yourself to spin a higher cadence, start in small increments. Find your natural cadence (the cadence you would spin if you were just riding with no biofeedback about your cadence). Then, for five minute intervals, try to add 5-10rpms. Recover and repeat. Soon your natural cadence will be higher.

If you're bouncing, it most likely indicates a lack of muscular strength (natural with a beginner). Because you're not strong enough to spin a high cadence with a harder gear, you spin an easier gear than you can biomechanically control (ie you bounce).