Reliable and accurate ultra-short-term prediction of wind power is vital for the operation and optimization of power systems. However, the volatility and intermittence of wind power pose uncertainties to traditional point prediction, resulting in an increased risk of power system operation. To represent the uncertainty of wind power, this paper proposes a new method for ultra-short-term interval prediction of wind power based on a graph neural network (GNN) and an improved Bootstrap technique. Specifically, adjacent wind farms and local meteorological factors are modeled as the new form of a graph from the graph-theoretic perspective. Then, the graph convolutional network (GCN) and bi-directional long short-term memory (Bi-LSTM) are proposed to capture spatiotemporal features between nodes in the graph. To obtain high-quality prediction intervals (PIs), an improved Bootstrap technique is designed to increase coverage percentage and narrow PIs effectively. Numerical simulations demonstrate that the proposed method can capture the spatiotemporal correlations from the graph, and the prediction results outperform popular baselines on two real-world datasets, which implies a high potential for practical applications in power systems.