The Navy will accept Nursing students in BSN programs. The program however, is highly competitive. You would be commissioned as an Ensign at a base pay rate of about $2900/month, after graduation. On top of the $2900 dollars you will also receive a housing allowance (depends on area but mine is around $1400/month), and other allowances. There is ample training opportunities and programs for furthering your education (up to doctorate programs).
(From Website)For the Nurse Candidate Program (NCP), you can get an initial grant of $10,000, plus a stipend of $1,000 per month for up to 24 months. That’s up to $34,000 to help pay your way through nursing school
Nurse Candidate Program