I would not worry about a dedicated detail rig starting out. Doing what Mikenap does is plenty and it works. Some people will say that it isn't very professional but to me, those who say that are usually those who have full out nice rigs and all the high tech equipment that they rarely use on every job. There is no reason/need to haul around an entire trailer or van full of stuff you may not even use that day. As long as you use good materials, reliable tools that get the job done right, that's all you need. If I were you, I'd offer pickup and delivery on full details and stuff that would be worth your while. If they are small basic wash and vacs then I'd run to their location and do the job. Throw most of your things like degreaser, car wash, spray wax, etc in gallon jugs, throw a few gallons of distilled water in there and then the rest of your equipment. This is pretty much what I did before I got a full shop. I did and still do mostly pick up and delivery and the customers love it. They prefer I take their vehicle back to my shop or back then to my garage. If you do the work at their place, they usually do not mind using their water and electricity. Just ask before doing the job so you know.
It can work and there's plenty of people here to prove it. Good luck and I hope it works out for you! As for you being in NC, I was thinking about holding some kind of thing at my shop for all the local detail guys to get together, bring their cars/hot rods, etc and hang out and talk about detailing. I am sure there are some out there who wouldn't do it because they think it's their competition but I know a few who would. Seems to be a handful here from NC and SC.