I never considered the Rodanthe/Waves/Salvo area as being "bike friendly" but maybe things have changed since my last visit. There are some paths and trails in various spots, but how good they are for biking, I don't know as I've never biked there.
Once you're out of Rodanthe/Waves/Salvo, NC-12 is the only road and a 55mph zone. The road's pavement (berm) at Camp Hatteras extends a up to a few feet beyond the marked travel lanes. I've seen folks ride bikes (and walk, myself included) on the berm, but there's little "margin for error" which makes it easy for you and/or a vehicle to accidentally drift into the others path at the wrong time. Beyond the berm is often very soft sand that is known to have swallowed many an unsuspecting visitor's car up to its axles. A word to the wise- be careful if you have leave the hard surface. Also watch for sand that has been blown onto the road as it can create a dangerous skidding situation similar to hydroplaning. During storms, water on the roads is a problem too because there are few places for it to drain.
From the Camp Hatteras, the closest towns with a full service grocery store (like a Food Lion) will require a ride of about 25 miles south to Avon or north to Nags Head. It's all federally owned land (Cape Hatteras National Seashore) between Rodanthe/Waves/Salvo and either Avon or Nags Head so there is no commercial development except for the marina at the north end of the Herbert C Bonner bridge. Therefore I suggest you bring with you the food you'll need for your entire stay as there are only "mom & Pop's" and convenience stores near the campground. Of course, if you only have a short list, it's better to buy local and pay the price than make a 50 mile round trip that will take up about two hours of your precious time.
If you need something camping related, take a walk down the beach (it's safer) to the Cape Hatteras KOA's camp store. It's bigger and historically, is better stocked than the one at Camp Hatteras.