Well it's complicated. But yes there are charges involved. You are not charged for the blood itself, but the process in ensuring that the blood is safe, available, and transfusable. Blood transfusions can be quite costly, so it's important for a physician to ensure the transfusion is actually warranted.
Hospitals do NOT receive blood from blood suppliers for free. The blood supplier charges transfusion center blood banks for the cost of donation, manufacturing, and transportation involved.
Red Blood Cells are typically purchased by a transfusion center from a Blood Donation Center at around $200-300, platelets can be roughly $600, plasma units can be $40-60. The final cost to the patient may be up to 4 times this amount. These charges from the blood center and transfusion center are not intended to take advantage of the patient, but there are many costs involved from donation to transfusion.
The blood center must hire employees to run the blood drives and process the units. Every donation must have infectious disease laboratory testing performed on it. Every donation must have a Blood Type performed on it. Individual component processing, tubings, bags, anticoagulants, shelf stability additives, bacterial testing, leukoreduction filters, transporting blood to the hospital or other transfusion centers, these all come at a cost.
A single transfusion of Packed Red Blood Cells can cost over $1000 after all of this work is performed.