Cleaning ; hand work. Gum bleeding ; swelling are the result of dental plaque (bacteria) not being removed from the teeth/gums. First you need a professional teeth cleaning to remove tartar (calculus) which is sharp/irritating to the gums. Next comes dedicated work by you at home. This is done by proper brushing, flossing, and use of anti-bacterial mouth rinses. Your gums will bleed at first but will stop in few days.
Bleeding gums. Bleeding and swollen gums is a sign of moderate-advanced gum disease. The first step is to see a dentist and have your condition evaluated, upon which treatment will be recommended. After having your teeth cleaned, follow the dentist and/or dental hygienist's instructions for brushing, flossing, and diet.
See a dentist. A professional cleaning, scaling and evaluation are critical to dealing with plaque. Proper home care instructions and cooperation will be the next step in moving forward.