Nothing. It costs nothing for a case to go to trial whether or not one of the parties asks for a jury.
A party who files a lawsuit does have to pay a fee for filing the lawsuit. As of this writing, the fee in North Carolina for filing a superior court case is $200. However, once the case goes to trial, there are no additional charges that the litigant has to pay the court for use of the courtroom, cost of the judge or the jurors. It does not matter how many days it takes to try the case, the cost is the same. The initial court cost is the only fee to pay to the court.
This is one of the instances in which the most valuable rights we have are basically free. The right to a jury trial is free in North Carolina, and in virtually all other states.
Even if the party who files the lawsuit ends up losing, he or she does not have to pay any additional court costs.