One of the bigger expenses will be doing things. There isn't a whole lot thats "free" in the USA as far as activities go. If you just want to ride around the country for a year and live in a tent it could be done for about $20 a day as long as you aren't a picky eater and dont put huge mileage on everyday. Shit adds up quick though, a six pack here, admission to something there, etc....spread out over a year can easily be thousands of dollars.
ETA free legal camping east of the Mississippi can be hard to come by compared to the western states