First, are you set on one service over the other? Navy Nursing, AF Nursing and Army Nursing are not exactly the same. Close- but different duties, type of locations (field medical centers, brick/mortar hospital, flying nurses, etc...). If you are not set on one or other, just want to service. Apply to all three - ROTC programs, this will increase your odds. My DD is trying for the NROTC Nursing Option as her plan A. She has researched and Navy is all she wants - but everyone is different. If you don't get ROTC, have a plan b, c, d, etc... First I am familiar with the Navy options. Navy has two other paths towards commissions as a Navy Nurse - do a little research with google for exact details but roughly: 4 year scholarship (NROTC - Nursing Option), Navy Nursing College program (apply between sophomore and junior year in college) - receive an "initial" bonus - in 2 payments, which helps towards the expenses of school, receive up to 24 months of monthly stipends to help the cost of your education. Upon completing of BSN - you attend OCS and are commissioned. The third choice, you pay for college (BSN at an approved accredited school), upon completing of BSN - you apply and are accepted for OCS/Commission. There are other options: If you want to be a Nurse and want to service, but military isn't a choice.
There are programs under the NHSC (National Health Service Corps) and NURSE Corps scholarship Program that help you with the cost of education and you would "serve" as a nurse in various health care facilities. (Another way to serve as a Nurse, if the military is not an option). CaptMJ has posted some great links. Research, research, research...nursing is a great field and there are opportunities - it just takes some digging to find the one that fits you.
Understand NROTC Nursing Scholarship - has been the lowest of all three services with only 19 a year in the past few years, AROTC and AFROTC have roughly the same amount of scholarships in the past two years - that doesn't mean it wouldn't decrease as noted above. Just make yours plans, but have plan A, B, C, and such, just in case.