Federated Learning (FL) enables collaborative training across decentralized data, but faces key challenges of bidirectional communication overhead and client-side data heterogeneity. To address these challenges, we propose pFed1BS, a novel personalized federated learning framework that achieves extreme communication compression through one-bit random sketching. Specifically, clients transmit highly compressed one-bit sketches of local model parameters, while the server aggregates these sketches into a global one-bit consensus vector and broadcasts it to all clients. For data heterogeneity, we introduce a sign-based regularizer into the objective function, guiding the optimization of personalized models that simultaneously align with the global consensus and preserve local data characteristics. To mitigate the computational burden of random sketching, we employ the Fast Hadamard Transform as an efficient projection mechanism, achieving near-linear computational complexity concerning the model dimension. Theoretical analysis guarantees that our algorithm converges to a stationary neighborhood of the global potential function. Numerical simulations demonstrate that pFed1BS substantially reduces communication costs while achieving competitive performance compared to advanced one-bit FL algorithms.