In this work, we propose a frequency bin-wise method to estimate the single-channel speech presence probability (SPP) with multiple deep neural networks (DNNs) in the short-time Fourier transform domain. Since all frequency bins are typically considered simultaneously as input features for conventional DNN-based SPP estimators, high model complexity is inevitable. To reduce the model complexity and the requirements on the training data, we take a single frequency bin and some of its neighboring frequency bins into account to train separate gate recurrent units. In addition, the noisy speech and the a posteriori probability SPP representation are used to train our model. The experiments were performed on the Deep Noise Suppression challenge dataset. The experimental results show that the speech detection accuracy can be improved when we employ the frequency bin-wise model. Finally, we also demonstrate that our proposed method outperforms most of the state-of-the-art SPP estimation methods in terms of speech detection accuracy and model complexity.