Hey, congrats on working towards the BSN. I have the same aspiration as you, but the army path towards the CRNA certification is the last option for me.
If you are a good student (you would have to be if you want to be a CRNA) there is no reason why you cannot get in at a civilian school somewhere in the US.
The reason why I discourage the ARMY/NAVY is because I feel there is no reason to put your life at risk, and also you will be away from family and friends, not to mention girls.
CRNA for civilian schools is not so bad dude, 3.5 gpa at least, good score on the grad test, and some experience.
cheers.