Bug reports, encompassing a wide range of bug types, are crucial for maintaining software quality. However, the increasing complexity and volume of bug reports pose a significant challenge in sole manual identification and assignment to the appropriate teams for resolution, as dealing with all the reports is time-consuming and resource-intensive. In this paper, we introduce a cross-project framework, dubbed Mutualistic Neural Active Learning (MNAL), designed for automated and more effective identification of bug reports from GitHub repositories boosted by human-machine collaboration. MNAL utilizes a neural language model that learns and generalizes reports across different projects, coupled with active learning to form neural active learning. A distinctive feature of MNAL is the purposely crafted mutualistic relation between the machine learners (neural language model) and human labelers (developers) when enriching the knowledge learned. That is, the most informative human-labeled reports and their corresponding pseudo-labeled ones are used to update the model while those reports that need to be labeled by developers are more readable and identifiable, thereby enhancing the human-machine teaming therein. We evaluate MNAL using a large scale dataset against the SOTA approaches, baselines, and different variants. The results indicate that MNAL achieves up to 95.8% and 196.0% effort reduction in terms of readability and identifiability during human labeling, respectively, while resulting in a better performance in bug report identification. Additionally, our MNAL is model-agnostic since it is capable of improving the model performance with various underlying neural language models. To further verify the efficacy of our approach, we conducted a qualitative case study involving 10 human participants, who rate MNAL as being more effective while saving more time and monetary resources.