I feel your pain, honestly I like abusing my gums with a harsh toothbrush on my teeth I rarely brush but good lord do I floss.. (My teeth are lovely and I dip tobacco, dentists compliment my healthy not pure white smile.
If you brush regularly at least once or twice a day? Use a soft toothbrush. If your gums are bleeding regularly use a good oral rinse. Personally I suggest the "Smart Mouth" brand it, it works but is 12 dollars a bottle at least here. It's pricey for a mouth wash but it works. It'll work the first time you use it and you'll notice.
I'm not advertising its just as a tobacco dipping areshole flosser who sucks blood out his teeth randomly I know it works.
I can't believe I'm the only one that hasn't noticed "The gum disease known as gingivitis" public broadcast commercials stopped existing in the 70's. We got stuff now that works. lol
Blood is a sign of gum disease but the remedy is good oral hygiene. Do you floss? This is essential. It very well may bleed initially. But the more you do it, the less blood you have and the better recovery of your gum tissue. This is my suggestion for working on your gums.