There is not enough information given in order to give you a more accurate idea of cost. Rates depend on your state that you live in. Do you have dental insurance? If you have dental insurance or a plan this a course would save you some money.
The type of cleaning that is normally done for gingivitis is what we would call a deep cleaning. A dental term would be gingivectomy and generally charge per quadrant (you have four quadrants in your mouth)
A rage of cost can be any where from $100.00 or more per quadrant.
to get a more accurate state range you can go to
http://www.insurancecompany.com Just key in you zip code.