Hello
The gum bleeds as there is some inflammation with the gums. this is usually because of the deposits that is there on and in between teeth. these deposits are known as Tartar, plaque. plaque are soft which you can remove by brushing it self. so, ideally the next step is to
1) improve brushing. and use soft tooth brush while brushing. and don't stop brushing even if it bleeds but be gentle. You SHOULD NOT APPLY PRESSURE WHILE BRUSHING.
2) do warm salt water rinse - in a warm water put 1 teaspoon salt and rinse nicely. you can do this 2-3 times a day.
Next Steps
if the bleeding still persists after 10 days . kindly visit the dentist as then there will be tartar which can't be removed with brushing alone it need professional clean up.
Health Tips
kindly visit dentist once a year to avoid such problems. hope this was helpful