I just thought I would throw my two cents into the conversation. I just graduated with my BSN (and just passed my NCLEX yay!!!), and I had the good fortune of discovering that I loved learning about the connection between health and policy. So, I applied for my MSN/MPH degree while I was in my last year of my BSN. Now, I am starting graduate school in two weeks. I am interested in working in Washington DC in on health policy issues, and getting my Ph.D.
There are lots of nurses who transition from direct patient care into forming policy. I would say that getting nursing experience is valuable, but I disagree with the notion that it is absolutely necessary before getting your MSN/MPH. I tend to stay away from advice telling me what I cannot do, I am just too positive for that. You can make whatever you want work for you, period. You can always get work experience while you are attaining these degrees, which is what I am doing. Also, I was very active with my community and on campus when I was attaining my BSN, so I had plenty to talk about on my personal statement. You have worked in an Neuro ICU, as well as your clinicals, and you can always talk about that.
So, it really is your choice, but follow your own instincts. I am at an age where I did not want to spend a year working only, when I could be working and going to graduate school. You can do whatever you want to do!!