I'm pushing 100,000 miles.
I've run into many women.
On my first cross-country trip, I ran into a solo woman finishing her cross-country trip on my first day out. She gave me advice about putting a wet sock around my water bottle - advice I still use today. Later, I met a Japanese woman heading westbound at the former Cincinnati hostel. We went out clubbing and traded notes on the route ahead.
I met a group of women touring in eastern North Carolina. Their group leader went to get some munchies and they snuck out the cigarettes. I met a woman touring up the Alaska Highway and we rode together for a while. I met a woman at Mercey Hot Springs and we rode across the Central Valley before heading our separate ways.
On my first full day of my 2005 tour, I rode with a woman who was riding the Pacific Coast. We met at the Pigeon Point hostel. I couldn't have asked for a better touring companion for that first day.
http://www.crazyguyonabike.com/doc/p..._id=26285&v=RZ
I'm not sure why you don't encounter solo women - since they are clearly out there. Granted that there are not as many - and granted that women face greater risks in a society that is anything but equal in terms of personal safety.
Then again, (if you are a guy - I am not sure)
I suspect that I go to a different church than you do -
and that may have a bit to do with approachability.