There's no average cost for natural gas heating as the natural gas bill will depend on your natural gas costs and how big of a house you have as well as how warm you keep your home in the winter.
My house is around 1,000 Square feet and I keep my house at 70 F when it's really cold out and my gas bill comes in at $200.00 per month and that includes all the other taxes and fees.
I pay $20.00 per month whether I use any natural gas or not.