The bleeding gums is usually due to inflammation in gums (known as pyorrhea in layman language) which is technically called gingivitis. This inflammation usually occurs because of plaque deposition, which is due to inadequate and inefficient brushing. When this reaches the supporting bone , it leads to mobility in teeth & this condition is called periodontitis.
Next Steps
What next is a generalized cleaning of teeth (technically called scaling/oral prophylaxis). A proper gum treatment along with some medication & local application gel & mouthwash is the complete solution.
Health Tips
Take good care of oral hygiene & visit the dentist every six months for routine checkup and professional cleaning.