How to avoid sore nipples while riding
This happens to runners more than bikers but is the same thing you describe... friction. 

I've done band-aids, tape and even special products (Nipguards) made for covering just the nipple area but the best remedy I've found is compression clothing. Even in the middle of summer, I will wear some skin tight Under Armour shirt. Heat Gear (odd naming, but actually cools the skin too) in the summer just to prevent friction between cycling jersey and the nipples. I'll switch to their cold gear during the winter, but always wear something skin tight under my upper layers.