Accurate short-term load forecasting is crucial for efficient grid dispatching and secure operation. Current methodologies predominantly employ centralized training of deep learning-based forecasting models. However, centralized data collection may violate data privacy regulations enforced by power utilities. To address this issue, this paper proposes a secure federated learning based bidirectional long short-term memory network (SFL-Bi-LSTM) to achieve privacy-preserving short-term load distributed collaborative forecasting. Specifically, SFL-Bi-LSTM incorporates a bidirectional long short-term memory network to comprehensively capture temporal features by simultaneously modeling forward and backward time dependencies, thereby enhancing prediction accuracy. To preserve data privacy during collaborative model training across multiple utilities, federated learning (FL) replaces centralized data collection with aggregated model parameters, ensuring raw load data remains local. Furthermore, homomorphic encryption is integrated to enable secure federated aggregation through ciphertext computation, effectively preventing potential reconstruction of raw load data via model parameter inversion attacks. Experimental validation on public datasets demonstrates that the proposed SFL-Bi-LSTM achieves a mean squared error of 2.0229 MW in distributed collaborative forecasting while maintaining data privacy. Compared to conventional methods, it reduces the average mean squared error across different utilities by 19.89%, demonstrating its generalization capability.