Most of the times, bleeding during brushing is a sign of gingivitis. It is a disease of your gums where the tartar and the bacteria build up on your teeth and cause swelling, redness or bleeding. Initially it shall be only during brushing, and if not treated, there might be bleeding in your saliva when you wake up in the morning or when you chew.
Next Steps
Get a thorough scaling done from a dentist.
Health Tips
Please do not stop brushing because it is bleeding. It will worsen the problem.