The advent of intelligent mobile applications highlights the crucial demand for deploying powerful deep learning models on resource-constrained mobile devices. An effective solution in this context is the device-edge co-inference framework, which partitions a deep neural network between a mobile device and a nearby edge server. This approach requires balancing on-device computations and communication costs, often achieved through compressed intermediate feature transmission. Conventional deep neural network architectures require continuous data processing, leading to substantial energy consumption by edge devices. This motivates exploring binary, event-driven activations enabled by spiking neural networks (SNNs), known for their extremely energy efficiency. In this research, we propose a novel architecture named SpikeBottleNet, a significant improvement to the existing architecture by integrating SNNs. A key aspect of our investigation is the development of an intermediate feature compression technique specifically designed for SNNs. This technique leverages a split computing approach for SNNs to partition complex architectures, such as Spike ResNet50. By incorporating the power of SNNs within device-edge co-inference systems, experimental results demonstrate that our SpikeBottleNet achieves a significant bit compression ratio of up to 256x in the final convolutional layer while maintaining high classification accuracy with only a 2.5% reduction. Moreover, compared to the baseline BottleNet++ architecture, our framework reduces the transmitted feature size at earlier splitting points by 75%. Furthermore, in terms of the energy efficiency of edge devices, our methodology surpasses the baseline by a factor of up to 98, demonstrating significant enhancements in both efficiency and performance.