Bruising around the site of a blood draw is a very common phenomenon and should not prompt immediate concern. When a vein is accessed for a blood sample, a small portion of blood may leak into the surrounding skin as the needle is withdrawn. This may happen more frequently with larger gauge needles or with "a difficult stick" - i.e., multiple attempts to draw the blood are made unsuccessfully prior to a successful draw.
If you have noticed that you have a history of easy bruising (significant skin changes with very minor trauma), however, this is a different concern. Easy bruising can be a sign of underlying problems with platelet function or number or the clotting cascade. Your primary care physician
should be able to run some blood work or refer a patient to a blood specialist to help determine the etiology of easy bruising.
If you have any concerns about your ability to heal wounds or easy bruising or your health in general, then you should seek out the guidance of your primary care physician.