I'm thinking that the bean plants will have a difficult time grabbing the strings if they're swaying in the wind.

I have rebar on the top and bottom to attach the vertical twine to but you can just use twine on the bottom to attach the verticals if you want. - Dick

Unless I miss my guess, there can be some pretty strong storms in Charlotte... so personally, I would recommend some form of anchor at the bottom of the strings. I agree with the reason given by Drloyd, it would be difficult to get the vines started onto a string which moves in the breeze.

Additionally, when the vines are fully leafed out & heavy with pods, a strong wind could easily cause the string to pull the plants out of the ground... or snap the string. I had this happen even when using a top & bottom string; strong winds caused the verticals to slide along the twine to one end, and either broke off or uprooted several plants.

For that reason, if using a trellis, I recommend that the material used for top & bottom support should have a rough surface. Rebar rod works well for that purpose (it is my method of choice) as would reenforced cotton clothes line or rope. If using poles, the strings can be tied off to stakes driven into the ground.

Been there, done that, got the t-shirt. A strong wind blew across my garden hard enough to rip plants out of the ground. Attach your trellis at both top and bottom. It will save you a lot of grief. I've never had my t-post, electric fence wire, and hay twine trellis damaged by wind. A tornado could do it, but if a tornado comes through, I have other things to worry about.