Hi Michigan 94,
It takes a lot of courage sharing something like that. So first off I would like to commend you for it. I think that a lot of nurses, including myself, struggle with depression type issues. It really helps me to know that there are others like me. With that being said I think honesty is the best policy. I would probably say something along the lines of having a medical condition that required you to miss work and leave it at that. Depression is actually covered by FMLA, but I assume you did not qualify for it yet as you had not been there long enough. When you say it is your fault, I disagree to a certain extent. I can't think of a situation where a mental illness like depression is someones fault. It is a mental illness that some people are born with. I think some people do not put a great emphasis on mental health and think that if we are not physically ill then we are fine. I am sorry you had to go through this and if they could not work with you due to a mental illness then you may not have needed to work there anyway.
Be good to yourself and fight the shame by bringing it to light with people that you trust. Take responsibility for anything that is actually your fault and leave the rest for others to take responsibility. We do not have to carry the blame for others' shortcomings.