This paper presents an approach for instantaneous bandwidth estimation from level-crossing (LC) samples using a long short-term memory (LSTM) encoder-decoder architecture. LC sampling is a nonuniform sampling technique that is particularly useful for energy-efficient acquisition of signals with sparse spectra. Especially in combination with fully analog wireless sensor nodes, LC sampling offers a viable alternative to traditional sampling methods. However, due to the nonuniform distribution of samples, reconstructing the original signal is a challenging task. One promising reconstruction approach is time-warping, where the local signal spectrum is taken into account. However, this requires an accurate estimate of the instantaneous bandwidth of the signal. In this paper, we show that applying a neural network to the problem of estimating instantaneous bandwidth from LC samples can improve the overall reconstruction accuracy. We conduct a comprehensive numerical analysis of the proposed approach and compare it to an intensity-based bandwidth estimation method from literature.