Unknown salt formed from electrolysis of urine
The main components of urine are water and then urea.  Water makes up 90% to 95% of urine with urea making up about 50% of the remainder.  It's likely that your reaction is mainly the hydrolysis of water.  In that case, you are forming hydrogen gas at cathode and oxygen gas at the anode.  Also, some $\ce{NaCl}$ will be electrolyzed and form $\ce{Cl2}$.

As you stated, you are likely oxidizing copper, probably making $\ce{CuCl2}$.  Most zinc salts that you could be forming in your reaction would be white.  If urea is being electrolyzed, then you would also be forming nitrogen and carbon dioxide at the anode.  It's possible that at least some of the migrating bubbles contain $\ce{Cl2}$ gas which then could form solid $\ce{CuCl2}$. 

You could do a quick test of some aspects of my answer by observing the hydrolysis of water using your system.  Just conduct your procedure exactly as you do for urine, but instead of urine use water.  The main salt present in urine is $\ce{NaCl}$, whose concentration varies quite a bit but is on the order of 3 g/L.  So just conduct your experiment on a 3 g/L $\ce{NaCl}$ in water solution and compare your results to the urine experiment.