Out of curiosity, in what ways are you feeling unstable?

I'd suggest, first, that you make sure the bike is set up properly for your body and riding preferences. Being balanced on the bike fore and aft will contribute to your sense of stability and give you better handling. A smooth pedal stroke, relatively fast cadence (I'd suggest 80 to 90 rpm as a starting place, but you might need to work up to that) and a relaxed upper body (don't grib the bars) will help.

Those are the things that occur to me off the top of my head. Mostly, it just takes practice.