Hi!
I am a fairly-new grad. I graduated September 2016, so by the time I start MPH, I will have one year experience. I do see that the experience is incredibly important but also think going straight from BSN to be ideal for me. I wrote my NCLEX November 2016 after travelling for a month, so yes I did have my CRNBC license when I applied. It sounds as though you a great start to your application, experience in research is valuable.
I wouldn't worry about acceptance rates, but more on cultivating your own application. I think nurses (along with all health practitioners) have a wealth of incredible personal experiences that make them ideal candidates to delve deeper into the complexities of public health! London School of Hygiene has a distance MScPH that is apparently really great. The school has a really great reputation on the international level. I'm tempted!