Is it normal for an industrial piercing to bleed almost a week after its been done?

Bleeding is normal for any piercing. A piercing is a wound, and wounds bleed. The only way it would keep bleeding rather than heal is if you pick at it or play with it. Dont play with it! Also, do not overclean it. Dont clean it more than once per day, and clean it with antibacterial soap. If you are using salt soaks or salt water, stop!! This is irritating to your piercing and can severely dry it out.