As a donor, I chose to not go thru a milkbank because of the tests and forms to do.
As part of my prenatal screening by my OB, I had the Hep B test done, but not HIV (is that weird?). I did have a blood donor card (I give blood regularly) and since they test for HIV, that seemed to be enough for the recipients. I was more than willing to provide all the test results that had already been done by my doctor.
Honestly, I probably wouldn't have gone for more blood tests had the recipients asked. It would be too time consuming. I don't have a baby sitter (nor would I want to leave my ds with someone at this point unless it was my dh) and the nearest place to get tested is 20 miles away. (Though if the lab is open on Saturdays, that might make getting tested easier.)
Having said that, do what make YOU feel comfortable. I know if I were on the receiving end, I wouldn't want to worry about whether the bm is disease-free.
Good luck.