To answer your question, whether or not you are able to apply to a DNP program before graduating all depends on the program you are applying to. So, yes you can, but only to the programs that allow that. You will find that programs will do one of two things: 1) allow direct admission in which you may apply before graduating from your BSN, or 2) they require 1-2 years of experience as an RN, which means you would not be able to apply before graduating from a BSN program, unless you had already gained the experience as a associates degree. Some DNP programs are built to be a completion after an MSN. There is a very wide variety of type of these programs with different focus areas and such. Before I began the application process, I emailed a list of questions to a number of schools in Wisconsin. One of my questions was whether or not direct admit student from a BSN program would actually have a shot at admission. The response from each school was that their DNP cohorts was a good mix of fresh BSN graduates and experienced nurses. Another piece of feedback I got from numerous people is that if you would like to function as an acute care nurse practitioner (in-hospital), you will certainly wish you had hospital experience as an RN, and success is difficult if you do not. However, FNPs in clinics is a different story- so I am told. You still need to have very sharp assessment skills that can be gained from a year of hospital experience, but you are playing a different game than an acute care NP.
-Identify exactly what you want to do as an NP, and read/talk to people about whether you should wait a year or so before attempting DNP school.
-Focus very heavily on assessment skills, pathophys, and pharmacology while you complete your BSN: ask questions, and always figure out the "why?" behind everything.
-Research the admission requirements for a few schools that you would consider applying to for DNP.
-Email their admissions office a list of any questions you may have.
-Seek mentorship from current professors or nurse practitioners you know.
I did all of those things and it definitely was very valuable. I am still waiting to hear back from the school I applied to. They interviewed 100 and admit about 25, and I should hear about in about 2 more weeks. I'm trying to not get my hopes up, but I did give it my best shot.
I hope this helps!