How do your gums bleed? the bacteria/plaque cause swelling/discoloring/bleeding of the gums?

Yes: In simple terms, the bacteria use food debris not removed to live on and release toxins that irritate the gums causing bleeding, inflammation and swelling. Eventually it goes further down and destroys bone and the supporting structures of the tooth.

Inflammation: Bleeding is caused by your body or host reaction to the foreign product (plaque and calculus), bacteria or bacterial product that accumulate in your gum and cannot be drained. Vasodilation of capillaries and developmental of granulation tissue in the socket, along with increase lymphocyte, neutrophile, macrophage, and along with compliment cascade. The result is the destruction of bone socket.