I know that the Charlotte Mecklenburg Animal Care has rabbits. I adopted a bunny from there years ago, but it looks like they only have a female right now. You could still contact them and ask to be put on a list if other rabbits (adult male) come in. You should also check petfinder.com. You put in the type of animal you are seeking and you can choose the gender and age too. Choose the 100 mile search to see more rabbits in area shelters and rescues.
I know that Carolina Waterfowl Rescue, outside of Charlotte (Indian Trail, NC), has taken in a few bunnies over the years, although they recently decided not to take them any more and concentrate on rescuing birds. They were looking for homes for the rabbits that they had left. I don't know if they have all been adopted or not. http://carolinawaterfowlrescue.com/index.html
Spartanburg Humane usually has rabbits, but they just have one female there now. They don't list on Pet Finder, so you have to go directly to their site or contact them. One of my rabbits was adopted from there. They unfortunately no longer spay and neuter rabbits.
Many of the rescues will adopt out rabbit to indoor homes only, but I doubt that any of the shelters/humane societies have that requirement. You can also speak to your vet or any rabbit vets in the area. Sometimes people who are looking for homes for rabbits ask their vets for help.
I know of a few vets in the Charlotte area, hopefully this list is still current. You may want to contact them to see if they know of someone looking to rehome their rabbit.
Griffin Avian and Exotic Veterinary Hospital
2100 Lane Street
Kannapolis, NC 28083
Dr. Lauren Powers
Carolina Veterinary Specialists
2225 Township Road
Providence Veterinary Association
6420-A3 Rea Rd.
Since your bunny is alone now, is there any way that you can bring her into the house?