I can't help you with Navy nursing, but I can help you with military nursing since I am Active Duty Air Force.
Anyways, there are definite advantages to military nursing, money for school, traveling, 30 days a year of vacation, decent pay, etc. But it's not all glamor. The biggest thing that civilians don't realize is the military owns you when you are active duty. For instance I'm not suppose to go more than 200 miles from base on my days off in case of a recall, meaning if a disaster strikes, we go to war, etc I have only so long to be at base in my uniform any time of the day. We are in a shortage also, you might get 30 days of leave a year, but you very well might be able to use it if you are short staffed.
Also, because of budget cuts (Thanks MR Clinton) themilitary has done away with most inpatient facilities. YOu migh be lucky like I was and wind up in one, but often you will work in a clinic doing telephone triage.
Now that I've battered the military let me tell you why I did it.
I'm proud to put on the uniform. You get such respect when someone sees you in it, it makes up for the response of "Oh you're a nurse" like I need pity or have the plague. I get respect from the docs for the most part. Because as a BSN you are an officer, the docs are officers, there is a certain amount of respect there that I have never found in the civilian world. The docs really do use your skills. It's how it's suppose to be.
And as for CRNA school, the AF also offers a program. Do realize any schooling you go to full time you will have to pay back to the military.
From what I can gather from other nurses, the Air Force treats its nurses better. The Army is suppose to be horrible. I don't know about any of that, but I would really research all of your options before you decide. Talk to other military nurses. It's a committment you can't easily leave. Once you sign up for 4 years it's very difficult to get out. That might not seem like much until your family wants to move, you want to move, you don't want to do this kind of nursing, etc.
Weigh all of your options. I might sound pessimistic, but no one explained this stuff to me before. I wish they had, the transition would have been easier.
Any questions, feel free to email me