Learning-to-learn (L2L), defined as progressively faster learning across similar tasks, is fundamental to both neuroscience and artificial intelligence. However, its neural basis remains elusive, as most studies emphasize neural population dynamics induced by synaptic plasticity while overlooking adaptations driven by intrinsic neuronal plasticity, which point-neuron models cannot capture. To address the above issue, we develop a recurrent spiking neural network with bi-level intrinsic plasticity (IP$^{2}$-RSNN). First, based on task demands, a slow meta-intrinsic plasticity determines which intrinsic neuronal properties are learnable, which is preserved throughout subsequent task learning once configured. Second, a fast intrinsic plasticity fine-tunes those learnable properties within each task. Our results indicate that the proposed bi-level intrinsic plasticity plays a critical role in enabling L2L in RSNNs and show that IP$^{2}$-RSNNs outperform point-neuron recurrent neural networks and self-attention models. Furthermore, our analysis of multi-scale neural dynamics reveals that the bi-level intrinsic plasticity is essential to task-type-specific adaptations at both the neuronal and network levels during L2L, while such adaptations cannot be captured by point-neuron models. Our results suggest that intrinsic plasticity provides significant computational advantages in L2L, shedding light on the design of brain-inspired deep learning models and algorithms.