Thanks for your post. I went to Yale for my MBA, and I think that is a good target program for you. Other programs you could research are HBS, Haas, Kellogg, Ross, and Duke. These each have a opportunities to study in the nonprofit areas, but you should research further to see which is the best fit for you.
You will want to be able to articulate your short and long term career goals – what kind of non-profit would you want to start, what would your role be? How would you grow it? What would you accomplish? Since you are making a career switch, you will want to think about which skills and experiences are transferable and demonstrate those in your application. Think about why this career change makes sense for you. With just three years of work experience, you will want to highlight your leadership abilities and maturity. Since you want to go into nonprofit management, and because it is an important factor for admissions committees, you will want to highlight your community service experience. This is another area you can demonstrate transferable skills and leadership. It is also a great way for you to get across your character and passions. You could also enhance your career plan story with your involvement in community service.
Insiders Guides: http://www.mbamission.com/guides.php?category=insiders
Free Consultation: http://www.mbamission.com/consult.php