I have a "volunteer" mulberry in my yard. For the past three years it has flowered and generated lots fuzzy/fluffy white things that look like will grow into actual mulberries. However they either get blown off by strong wind or rain. This year that didn't happen, but the they are drying up and falling off.
Your tree may be a female with no male nearby or a male that doesn't produce fruit. This site is from Indiana but has lots of helpful info to help you possibly id the type of mulberry you have. http://www.ces.purdue.edu/extmedia/FNR/FNR_237.pdf
