Do you now food when traped between your gum and tooth ( Pocket ) it gets detoriated and creates a pool where bacteria grow and produce acids which further causes inflammation of gums and results in gum bleeding.
We call it gingivitis...
What can be solution?
Reverse the story remove bacteria - remove food - keep good oral hygiene and bang on swelling and bleeding will vanish...
For me electronic Rotary brushes are fancy... if not used in correct way and angle they create more harm than benefit.
Better try traditional system of brush first.
Get interdental brush.
Use floss in correct way.
Use mouthwash.
Clean tongue.
Massage gums.
Gargle with lukewarm water.
Next Steps
Scaling ( teeth cleaning ) will help you.
Health Tips
understand there is no one time solution to stop bleeding as we are going to eat again, bacteria going to grow again and gingivitis may happen again... point is who wins
bacteria or hygiene?