Bleeding usually stops within a few days (if there is any) but it can go on for a week or even two without being a huge problem - as long as it isn't a whole lot of blood. What's happening with yours sounds pretty normal.
There are a few things you can look at to help stop it though.
What type of jewelry were you pierced with? If you have rings, they can move around and cause micro-tears in the healing tissue. Barbells are generally better for healing, but if you have rings, it's not a big deal (I healed mine with rings - had them done before barbells became the standard).
If you're not already, try sleeping with your bra on for a while. It will hold the jewelry in place and you won't catch the jewelry on sheets. It will also help cut down on the movement of your breasts while you sleep. You can place a piece of sterile gauze in each cup to protect your bra and keep the piercing clean.
Make sure you're not moving the jewelry when you clean them. Soap and rotating jewelry is out-dated aftercare, but is still recommended by some piercers. You don't need to do it. Just do sea salt soaks 2-3 times per day for the first few weeks, then you can drop down to 1-2 times per day. Mix 1/4 tsp sea salt with 1 cup warm water. It should taste as salty as your tears. More is not better. Just soak and remove any discharge with a q-tip after the soak, don't move the jewelry.
If you're still having some bleeding after a week or two, go back to your piercer and have them take a look at it.
And for the person who mentioned breast feeding, learn some basic anatomy before you comment. Nipple piercing does not affect breast feeding.