Did a month long tour of stealth camping everynight but one night where I paid for a site. The tour cost me about 12 bucks per day and I could have made that cheaper by not eating fast food and drinking sodas as much at conv. stores. I'm not a vegan though. Probably would be cheaper if I were so I wouldn't eat at McDonald's and Hardee's as much. My biggest mechanical expense was buying tubes for the flats. 3 bucks a tube.
I figure to be safe, cost of food per day plus 5 bucks a day goofing around money times the number days you will be riding plus emergency cash will be what you will need.
Basic bicycle repair is a must to know like replacing a pedal, chain, spokes, tires, tubes, lube, etc in order to keep expenses under control from having someone else do it for you.
The odds you are going to get caught stealth camping is minimal and the worse thing that usually happens is you are asked to leave. Just don't stealth were it clearly states NO TRESPASSING or you have to cross over a fence (implied trespassing) or at a public school or near a playground. I've never been caught.
I live in South Carolina and I wish you well in your journey here.