How can I learn to comfortably share responsibility with my nanny?

Personal boundaries. A lot of this depends on you, and what you ask the nanny to do. If the nanny is only there a couple hours, fine, no significant attachment. But if it's all day, this person is essentially a third parent, and it's important to not get jealous of bonds that they may form. If you trust your nanny to share your values, the child should be fine, and they will still love you and make strong bonds too.
When you are ready. It is natural for a mother to be protective of their child. Even though you picked a nanny for your family it is still going to be a struggle to completely let go. You should take it in the stages that you are comfortable with.