The best solution I've found for bleeding gums is oil pulling. After only 2 weeks I had significant improvement, stronger gums, and elimination of bad breath. I found olive oil, grapeseed oil, or sunflower oil to be best for curing gums. The basic process is to take a tablespoon of oil and swish in the mouth for 15 - 20 minutes, no gargling, and no swallow. I did for 4 weeks and it was hard to give up once started (addictive). After a few years, I usually do at least once per month, and my gums are still healthy.
Check the oil pulling forum on curezone for more info on how to do it properly.