Hi GrettaB,
After reading your post, I felt compelled to chime in. First, I do not work in the medical field and am only speaking by personal experience. I have suffered from anemia my whole life and had it rather severely the last year. My doctor put me on a very specific iron supplement. Anemia is caused by low numbers of red blood cells or concentrations of hemoglobin. Iron supplements are almost always used to treat this unless the anemia is very severe. If you are on an iron supplement, it is hopefully at the advice from your physician. It is not something to just "take", as it can be potentially toxic. Easy bruising is one of the symptoms of anemia and it is unlikely an iron supplement would actually cause bruising. In addition, iron has varying rates of absorbability. Not a whole lot is absorbed by the body unless you are being strategic about when and how and in what dosage you are taking. If your doctor did put you on it, you should consult with him/her to see if it's advisable to go off since the underlying health problems for anemia are low energy, hair loss, bruising, nose bleeds, and a whole host of other health problems.
RapidBreath made a good point. The bruising could be caused by either another supplement/medication that thins blood, or another health condition. Or it could be the impact of the exercise or even something else altogether. I think we all forget how much physical stress our bodies are under all the time. If it is happening to you a lot, the only way to be absolutely sure about what is causing it is to see your doctor and get full bloodwork done, a CBC, CMP and Iron Panel. If you've done this already, then you can explore other possibilities. Perhaps a sports medicine physician or an orthopedist. My physician is a combo -GP and Sports Medicine, which is handy since I am so physically active. Once you know, you can address and not stress!
I know I sound terribly preachy, but this is a topic near and dear to my heart as I have been living it. Hope my experience can help you a little. Good Luck!!
Elizabeth