I'm not sure this counts as a bias in healthcare, but I remember reading a study that looked at a large walk-in clinic that served a diverse population. A patient on any given visit would be seen by whatever doctor was next available.
They found that patients were more likely to follow the doctor's instructions after they left the clinic if the doctor was the same race as the patient.
Unfortunately, I think that's another reason we need to collect those statistics. Because if we can't measure the problem, we'll have a very hard time fixing it.