Modulo sampling has recently drawn a great deal of attention for cutting-edge applications, due to overcoming the barrier of information loss through sensor saturation and clipping. This is a significant problem, especially when the range of signal amplitudes is unknown or in the near-far case. To overcome this fundamental bottleneck, we propose a one-bit-aided (1bit-aided) modulo sampling scheme for direction-of-arrival (DOA) estimation. On the one hand, one-bit quantization involving a simple comparator offers the advantages of low-cost and low-complexity implementation. On the other hand, one-bit quantization provides an estimate of the normalized covariance matrix of the unquantized measurements via the arcsin law. The estimate of the normalized covariance matrix is used to implement blind integer-forcing (BIF) decoder to unwrap the modulo samples to construct the covariance matrix, and subspace methods can be used to perform the DOA estimation. Our approach named as 1bit-aided-BIF addresses the near-far problem well and overcomes the intrinsic low dynamic range of one-bit quantization. Numerical experiments validate the excellent performance of the proposed algorithm.