Nerve pain and "handedness"—is it common for your dominant hand to be more susceptible to nerve problems?
I don't know of a scientific study directly answering this question.  In leu of empirical (and verifiable) information, I provide an theory based on anacdotal experience.  


You generally use your dominant hand more off the bike than the non-dominant hand. If in your work or other activities you have poor posture or poor ergonomics your dominant hand may already have higher fatigue or irritation relative to your non-dominant hand.  This effect would be subclinical (i.e., either you don't quite notice, or its low enough you don't seek help).  Now expose both hands equally to a sustained level of irritation (e.g., poor bike fit) and the dominant hand will be the first to become "clinical."

Side Note

It could be worth looking on how you rest your hands on the bar (e.g., see Pain in center of hand).  I think many modern road bars have poor ergonomics for slower endurance riding, where you may be placing more weight on your hands. Also many riders have their bikes set up with the bars too low  for the majority of riding they do. This will put more weight on their hands and will quickly expose ergonomic issues. Personally, I find slammed positions fine if you are cranking out large wattage all the time (i.e., 250+ sustained), but it can cause problems for long rides at more moderate output (i.e., &lt;200 watts sustained)