Future Internet-of-Things networks are envisioned to use small and cheap sensor nodes with extremely low power consumption to avoid the extensive use of batteries. To provide connectivity to a massive number of these nodes, backscatter communication (BC) is emerging as an energy- and cost-efficient technology exploiting the reflection of radio frequency signals. However, challenges such as round-trip path loss and direct link interference (DLI) between the carrier emitter and the reader limit its performance. To tackle these limitations, this paper proposes a joint access point role selection and a novel beamforming technique for bistatic BC in a distributed multiple-input multiple-output setup. The proposed approach boosts the received backscattered energy while effectively mitigating DLI, thereby reducing the error probability. We also propose a channel estimation method tailored to operate under DLI conditions and propose a mismatch detector using estimated channel coefficients. Furthermore, we derive a closed-form expression for the probability of error for the detectors and model the quantization noise caused by DLI. Finally, comprehensive simulation results show that the proposed method with 1-bit analog-to-digital converters (ADCs) effectively mitigates DLI, reduces the quantization noise, and enhances backscattered signal energy, achieving performance comparable to the benchmark scenario with 8-bit ADCs.