Most backup camera systems use a standard NTSC composite video signal.
For integrated nav:
You will need to purchase some sort of video switcher/mixer (to combine/select the 2 video signals) and a compatible GPS system that outputs a composite video signal.
The Garmin GVN53 is the only GPS system I know of that outputs NTSC video:
http://www.garmin.com/products/GVN53
There are a variety of video switchers out there for car use. They are commonly used for in car entertainment systems. Try a local car audio shop.
All of this does not come cheap... the GVN53 is about $500 USD plus figure another $100-$200 for a video switcher. Figure $700 USD for the parts plus installation costs. You can buy a full featured touch screen GPS for a lot less.
Cost aside, another concern is screen size. I assume the Rogue comes with the small 2.4" review camera screen. This is way too small to make a GPS display legible. Even the most basic GPS systems use a 3.5" or 4.3" hi resolution screen.
As for bluetooth:
I have not seen something like you are describing. ie. Integrate Bluetooth with NTSC display. It may exist, I just haven't seen it.